Like many words, we can denote a strict sense, and a more relaxed colloquial sense. We can also note that the meaning of the words have changed a bit over time. 
 
The word monastery originally came from the Greek word monazein which means, “to live alone." In the earliest days monastics, (both men and women) went to the desert to live a largely solitary life in separate dwellings. However, many of them in a local area came to share some common buildings for prayer and eating. Over time many came closer together, and eventually were housed under one roof, though the monks and monastic sisters still tended to keep long hours of silence. Thus they lived in a relative, if not physical solitude, coming together also for communal prayers, meals and necessary community deliberations in the shared chapel, refectory, and chapter hall. 
 
Today the word “monastery” has tended to be used only of communities of men, while communities of women have tended to have their dwelling denoted as a “convent” or “cloister.” But, technically, there are women’s communities whose domicile is most properly termed a monastery. 
 
The main difference that the term “monastery” is meant to signify is that those who live there, live “alone” or apart from the everyday world. Their prayer is centered in the monastic community. Generally too, their work or apostolate is also centered there, rather than out in the community or world. Some enclosures are strict, others less so, but the concept of dwelling apart is key. 
 
“Convents” and religious houses, however, tend to house religious men and women who do not live and work in such isolation from the everyday world. Perhaps they work in education, hospitals or other external places during the day, but then return and live in community, sharing meals and prayer and other aspects of common life. The word “convent” comes from a Latin word which means “to convene or gather,” and is less inclusive of the concept of solitude contained in the word “monastery.” 
 
Historically, communities of men and women have used different terms to indicate “conventual” settings. Women’s communities have used terms like convent and nunnery, whereas for the men’s communities terms like priory or friary have been used. 
 
Nevertheless, and despite a variety of adaptations, the fundamental distinction to be observed is between communities (male or female) that live in some solitude (monastic) and those which interact more directly with the everyday world (conventual).

We don’t know. The story itself is very moving and there is naturally a human tendency to want to know more. Thus traditions and legends often set up in cases like these. But the historical accuracy of such things is often difficult to assess. “St. Dismas” is a name that tradition supplies us in the Western Church. However other names have also accrued to him in the East and in other eras such as Titus, Zoatham, Demas, and Rach. 
 
Interesting though these traditions are, we sometimes miss the main point when biblical figures are not named. For, if you are prepared to accept it, you are the good thief who “steals heaven,” if you are willing to repent, take up your Cross, be crucified with Jesus and persevere to the end, asking God’s mercy and admission to his Kingdom. 
 
The “good thief” was not so much good as he was smart. He knew that he was a sinner, justly condemned, and that his only hope was grace and mercy. Having repented, he turns (which is what “conversion” means) to Jesus and in faith seeks his salvation. Jesus says, “No one who comes to me will I ever reject” (Jn 6:37). And thus he is saved. Smart!

The happiness of heaven cannot be equated with earthly categories and prerequisites. Exactly how we will be happy in heaven cannot be explained to us here. Scripture describes heavenly happiness as: What no eye has seen, what no ear has heard, and what no human mind has conceived" -- these things God has prepared for those who love him (1 Cor 2:9). 
 
Jesus also cautions the Sadducees, who tried to project the earthly realities of marriage and family into heaven. He said You are in error because you do not know the Scriptures or the power of God (Matt 22:29). In other words, and for our purposes here, we have to admit that our grasp of what Heaven is, and how it will be experienced, cannot be reduced to, or explained merely in terms of how we are happy now. 
 
That said, some have speculated (and it IS just speculation) that the happiness of heaven, even despite missing family members, will be possible in light of the deeper appreciation of God’s justice that we will have there. Surely we will concur in heaven with all God’s judgments and in no way incur sorrow on account of them. 
 
Hence, we will see that those excluded from heaven are excluded rightly and have really chosen to dwell apart, preferring darkness to light (Jn 3:19). And while it may currently be mysterious to how this will not cause us sadness, God does in fact teach us that he will wipe every tear from our eyes (cf Rev. 21:4).