At the local nursing home, a religious Sister, wearing a traditional full habit, conducts a communion service. During communion the non-Catholics are also brought forward and she traces the cross on their forehead and says God bless you. Is this allowed?

​The conferral of a blessing, even with the sign of the cross, is not forbidden to the non-ordained in all circumstances. For example, parents should be encouraged to bless their children, even trace the cross on their forehead. In some settings and cultures, elders often bless youngsters. Laypeople even bless themselves whenever they make the sign of the cross. 
 
However, in the liturgical setting you describe, some parameters should be observed. The moment of the distribution of Holy Communion, at a Mass or communion service, is not really the moment for people to seek other sorts of blessings. In a Mass, the priest will surely give the general blessing at the end of the liturgy with the sign of the cross over the whole congregation. Hence, all those present will in fact receive a blessing. 
 
There are however pastoral concerns of how best to deal with a practice that has become widespread, and is not done in bad faith. Frankly, most pastors overlook the practice and when requested, confer blessings in the communion line. Even if they do dissuade their parishioners from the practice, many visitors still often come forward requesting blessings. Thus, the matter may better be resolved at the diocesan or national level. 
 
While the situation you describe is wrong, Sister is probably trying to make the best of a difficult situation wherein people expect such blessings, even if they are not Catholic. Finding a teachable moment to gently instruct the faithful is not always easy given the presence of many visitors. 
 
Nevertheless, the goal to move toward is to teach that the distribution of Holy Communion is not really the time to seek other blessings. An additional confusion is created when, though priests and deacons are present at Masses, laypeople at other communion stations are often giving out what appear to be priestly blessings. Finding a gentle way to clear up the confusion becomes increasingly important.