The Catechism says that sex must be ordered per se to the procreation of human life (# 2366). “Per se” does not mean every act can be fertile but only that “by itself” (i.e. per se) the act is not intentionally hindered from its natural ends. This is what contraception, homosexual acts, and certain heterosexual practices, that do not complete or naturally render the marital act, do. But it is clear to any biology novice that not every sexual act results in conception. 
 
Consider by analogy, that I call a friend, and this might result in speaking with her, or perhaps being sent to a voice mail. Whatever the final result, my reason and purpose for calling was to try to reach my friend. One would likely consider me a madman if, in dialing the numbers, I had no intent of reaching my friend, and was angry if she did pick up the phone and begin to speak. Whatever the final result, the calling of my friend is per se related to speaking with her. 
 
And this is what it means that marriage, and sexual activity, must be “per se” related to the procreation of children, even if the results of that activity do not always attain the full purpose of that action. 
 
Older and/or sterile people do not intentionally exclude one of the two fundamental reasons for marriage and sexual activity.

The practice you describe is allowed. In 1997 the American bishops received permission from the Congregation for Divine Worship for the celebration of funeral rites in the presence of cremated remains. 
 
There are some adaptions to the rites, however. The priest may greet the remains at the door and sprinkle them with holy water, but the covering of the remains with the cloth (the Pall) is omitted. The Easter candle may be placed near the cremated remains, but there was no mention of the priest incensing the remains. Otherwise, the funeral mass is celebrated as laid down in the Roman Missal and the funeral ritual. 
 
Prayers, which do not make reference to honoring the burying of the body of the deceased, should be chosen, instead of those, which have these references (cf Funeral Ritual #428). The prayers of final commendation at the end of the funeral mass are largely followed in the normal way. It is uncertain at this point whether the remains are to be incensed or not. It would seem this is permitted, but not required. The deacon or priest concludes the funeral Mass with an alternate dismissal listed in the rite, which makes no reference to the body. 
 
The forbiddance of cremation by the church in the past was due to the fact that many made use of it as a denial of the resurrection of the body. This is seldom the case today, but such an attitude must be ruled out before cremation is permitted. But note, "Although cremation is permitted by the church, it does not enjoy the same value as Burial of the body. The Church clearly prefers and urges that the body of the deceased be present for the funeral rites, since the presence of the human body better expresses the values which the Church affirms in those rites. (# 413)

Part of the answer depends on an important distinction, which many lose, in the Church’s teaching about stem cell research. The Church does not oppose all, or even most stem cell research. There are, for example, no moral issues with using stem cells harvested from adult humans, or from the umbilical cord after birth. It is only the use of stem cells acquired from human embryos, which the Church opposes, because it requires the killing of human life in order to obtain them. 
 
Hence, the company in question is not committing sin per se in supplying material for stem cell research. Only those who wrongfully use stem cells acquired from human embryos commit wrongdoing. 
 
However, let us suppose that it is clear to you that the company is certainly supplying some materials for the specific purpose of embryonic stem cell research. The morality of you accepting employment with this sort of a company would vary based on a number of factors. 
 
Let us presume, as is usually the case, that the pharmaceutical company is large and supplies a vast variety of pharmaceuticals for a wide array of medical purposes. In such a scenario taking employment with such a company would only involve you in remote material cooperation. And such associations, while not ideal, are morally permissible. 
 
However, if the position in the company that you are taking would require you to promote embryonic stem cell research to advance the sales of specific products related to embryonic stem cell research, such work would be of a more direct material cooperation. In such a case, you ought not take the job which would involve you directly advancing and cooperating in a moral evil. 

Well, I am not so sure. It's kind of like asking if Orville and Wilbur Wright would recognize the simple wooden and cloth plane they flew, compared to the modern jetliner of today. To some extent they certainly would see the basic structure, but they would also marvel at all the magnificent developments that their simple idea has ushered in. 
 
It would not be reasonable to assume that they would wag their finger and insist we go back to planes made of cloth and wood and gasoline motors. It seems more reasonable that they would admire the developments that have ensued, all of which built on the basic ideas that they set forth. 
 
I think it would be similar with the Apostles. It is clear that doctrine has developed over the years, as has liturgy and other necessary structures in the Church. But these things developed from the structures that were already there from the beginning. The seed of truth has become the mature tree. The hierarchal structure, established by Christ himself, has expanded to meet the needs of a now worldwide Church. 
 
You are free to consider things you don't like as pompous, but others see such things as dignified and appropriate. God, and the things of God, are rightly to be honored with some degree of ceremony and respect. 

It sounds as though you were describing the third-class relic. A first-class relic is some part of the body of a Saint, usually a fragment of a bone or perhaps a lock of hair. A second-class relic is some article owned by a canonized Saint, usually an article of clothing, or some other personal object associated with the Saint. A third-class relic is something, usually a cloth of some sort, which is merely touched to a first- or second- class relic. 
 
One may serenely dispose of third-class relics. Most piously and properly, this is done by burning or burying it. Merely pitching such things in the trash is probably to be avoided, though there is no absolute Church norm related to the disposal of third-class relics. 
 
The practice of mailing, or placing these third-class relics in the hands of the faithful may, at times seem annoying. But here too there are no absolute Church norms forbidding such a practice, or of mailing third-class relics. This is quite different from first-class relics, wherein significant church norms and laws are involved.

Your insight "once a priest, always a priest" is a correct one. Thus, a man who, "leaves the priesthood," is not leaving the priesthood, per se, but is setting aside the practice and discipline of the priestly ministry. 
 
For a priest to validly and licitly marry in the Church, he must first be “laicized.” That is, while his priestly character remains, he is permitted and then required to live as a layman in the Church. And so, except in very rare “danger of death” situations, he cannot hear confessions, or give anointing of the sick, and in nowise celebrate the Sacred Liturgy or exercise other offices related to the priestly ministry. 
 
Further, when laicized, he is usually dismissed from the discipline of celibacy and free to marry. Note that celibacy is a discipline. And while a common and expected discipline of most priests, it is not utterly intrinsic to the priesthood. There are married priests, most of them in the Eastern Rites of the Catholic Church. But even in the Western (Roman) Rite there are some married priests. Most of these have come over from Anglican or Lutheran ministry and were then ordained Catholic priests. 
 
Thus, when a man leaves the active priesthood, and is laicized, he can also have the discipline of celibacy relaxed for him by the Church, such that he can marry. 
 
It is certainly lamentable that some men do leave the priesthood, a ministry they agreed to accept for life. And yet the Church, as the loving mother, does make some pastoral provision for men who regrettably have need of leaving the active priestly ministry for grave reasons. These provisions are in place so as not to utterly lose them to the practice of the faith, and to hold them as close to Christ and the Church as possible.

Your answer is not far from the point. People often give the Church exaggerated power, as though she can do anything she pleases. But, as the last three Popes have all stated, the Church has no authority whatsoever to confer priestly ordination on women. This is because Jesus, though he broke many conventions of his day, nevertheless called only men to be apostles. And in the call of the apostles is the origin of the priesthood. 
 
The Church can no more alter the matter and form of this sacrament than she can use beer and pretzels, for consecration instead of bread and wine. There are just some limits we must observe.

To be supportive of the so‐called “right” to abortion is indeed sinful and erroneous. Further, to vote to fund abortions is indeed a grave sin. The degree of culpability will be based on how directly the legislator votes for abortion. To go directly to fund abortions is clearly a grave evil. Sometimes however, abortion funding is tucked inside omnibus bills. And thus the culpability of the politician involves a more indirect cooperation with evil. 
 
Bishops and pastors have a serious obligation to warn those who serve in public life against directly supporting, and especially funding, abortion. How this is best done is a matter of tactics and prudence. 
 
Consider for example that a man has some obligation to protect his family from home invasion. Theoretically, any number of alternatives might be possible for him. Perhaps he might booby‐trap his property with lethal weapons that would instantly kill any trespasser. On the other hand, he might reasonably conclude that such a method would also endanger others whom might happen upon his property. Thus he might use lesser means, such as alarms, extra locks, and warning signs. 
 
Which methods are employed, might vary from place to place. If a man lives in a country where civil wars are raging, he might use more severe methods. On the other hand, if a man lives where civil law is generally in place, he may feel it is reasonable to use lesser methods. 
 
It is the same with the bishops on how best to deal with dissenting and wayward Catholic politicians. In some cases, public disciplining and refusal of communion may make some sense. But in other settings, many bishops have concluded such measures might make martyrs out of such politicians. Perhaps the bishop will prefer to privately warn a pro‐choice politician that they will have to answer to God. 
 
Many, who are quick to critique the bishops, ought to recall that matters such as these require careful prudence. Many who demand significantly punitive measures do not themselves take this approach in dealing with their own families. The Lord himself warns that, sometimes in our zeal to pull up weeds, we end up harming the wheat. 
 
Reasonable people differ on how to handle matters of prudential judgment. Indeed, individual bishops vary in their approaches. This is the nature of such prudential judgments. Catholics do well to pray for priests and bishops, who have obligations to correct, but must do so in ways that do not cause more harm than good. Pray!

Context and content are important in answering a question like this. In the liturgical setting only a priest (and sometimes the deacon) should be conferring blessings since they are present and available for such. Thus, the practice observed in some places of lay people who are distributing communion and also giving blessings is inappropriate. The priest should be sought for this, apart from the communion line. 
 
However, in other settings lay people can give certain blessings in certain ways. For example, a parent can bless a child, an elder can bless a youngster, etc. In doing this, however, they ought to avoid priestly gestures such as making the sign of the cross over others. Perhaps tracing the cross on the forehead is enough, or simply laying a hand on the head, or no gesture at all, are better. 
 
In settings where lay people are praying for one another, say in a prayer for healing or deliverance, similar rules should be followed, avoiding overt priestly gestures, and being content to lay hands, or make no gesture at all. 
 
In the rare instances where lay people lead formal liturgical gatherings, such as the Liturgy of the Hours, they must not only avoid gestures, but also follow prescribed texts which merely ask God’s blessing on the assembled believers, but do not imply they are bestowing such blessings. 
 
Finally there are certain specific prayers and blessings that can only be given by a priest. The norms are too specific to be given here in a general answer. But most blessings of objects and sacramentals are reserved to clergy, and the laity ought to be content to offer simple prayers, asking blessings for one another only in appropriate contexts.

Yes, it is more of a quirk in the translation and of how we speak in English. There is only one resurrection. 
 
The English word “resurrection” comes from the similar word in Latin, “resurrexit” which can be translated “he arose” but more literally means “He stood up again,” for re=again and surrexit=he stood up. The Greek text of the Creed also uses this construction: ἀναστάντα (anastanta) means to stand up again, ana=again, stanta= to stand. 
 
Thus when we render these concepts into English we use the word “again” to capture more the sense of the Latin and Greek texts, which speak of the resurrection in very physical terms. While in English we could simply say “He arose” or “He rose from the dead” but, in a sense this is abstract and doesn’t quite capture the Latin and Greek which emphasize the physical fact that Christ who was freely struck down in death is now standing up once again. 
 
It is true that in English “again” can mean that someone has done something more than once, as in “He did it again,” implying that this is at least the second time he has done something. But “again” can also mean simply to return to a former state. As in “He is back home again,” meaning he who had left has now returned. It is this second sense of the word “again” that is meant when saying Jesus “rose again.” In other words, Jesus who once stood among us fully alive, is now doing so again.