Were there any special rules on how old someone had to be before taking on holy orders? Were there differences here between different monastic orders?
From the twelfth century on, period reform movements within monastic orders, or the foundation of new orders entirely, tried to eliminate the practice of child oblation. That is, when parents would pledge one or more of their children to monastic vows in a particular convent (a gender-neutral term here), and typically, the child would grow up in that community from elementary school-ish age onwards and then take vows--but not really have a choice in the matter. Child oblation was popular because many monasteries weren't simply "religious communities"--they were politically and economically powerful landholders, and having a family member in/running a community (oh, yes, noble families might even be able to control elections of priors and abbesses, good times) was pragmatically useful. There were spiritual benefits as well, of course--having a group of chaste virgins praying for your family's souls day in and day out was excellent insurance against extended stays in purgatory.
But monastic reforms in the later Middle Ages tended to stress the harshness of monastic life, its struggles and trials, and the importance of free and mature choice to follow this particular, prestigious, and not-at-all-for-everyone way of imitating Christ. From a theological perspective, therefore, this meant only allowing adults to enter the community and take monastic vows. From a political standpoint, of course, it was also to limit (definitely not eliminate) the secular ties of a given convent. The most famous example of this type of reform is the early zeal of the Cistercian order.
However, with the Cistercians and then with later orders that attempted the same restriction on young people's entry/rejection of child oblation, the initial commitment was always complicated, and then waned over time. The first problem, especially relevant for women, was education. The essence of the monastic life was singing the Divine Office--communal chanting of psalms and hymns at set times of the day, ever day. Individual reading (meditative reading as an act of prayer) followed closely behind as a goal, especially in some of the later reform movements. The first of these demanded Latin; the second invited it (although by the late Middle Ages, women's communities in particular often had rich libraries of vernacular devotional texts). And Latin, in the medieval mind, had to be learned in childhood.
For boys, there were both multiple ways to get a basic Latin education by the late Middle Ages, and alternatives to monastic life to do with that education. For girls, the choice was convent schools or a private tutor (the informal education groups seem to have been vernacular-based). And with a handful of exceptions for royal children, schools at women's convents were limited to future nuns. So a girl in school would pretty much be destined for life as a nun, even if not in the same quasi-legal manner as earlier.
The second problem was politics. Each wave of reform tended to get a LOT of attention and support from lay nobles, perhaps connected to their own religious zeal, perhaps because monastic reform movements often responded to some other social need (like the Franciscans and the Dominicans as urban preachers). Thus, lay nobles sought closer ties to and more power over the new convents. There was a slow, almost informal encroachment of the secular world into convents--sometimes brought by noblewomen or urban men retiring to one at the end of a healthy life, sometimes brought by a random five-year-old being dropped off at a monastery with no explanation given (Gertrude of Helfta, late 13C Cistercian, and Magdalena Beutler, early 15C Franciscan, both came to monastic life in this manner), sometimes brought by lay people securing extra privileges and comforts for family members in a community...cultivating closer ties between the members of a noble family inside and outside convent walls. Pledging children to a community, even if perhaps informally, was an important way of securing those ties.
Hence, of course, the frequency of new reform movements--both the establishment of new orders, and the reformation of houses in existing ones--that sought to strip out the encroachment of secular politics, comforts, and values.
Follow up: Was it any different for the Military Monastic Orders? Cause my homeboy Hochmiester Winrich Von Kniprode joined the Teutonic Order at 10 years old.
Oh, and a follow up to my own question: did the rules differ for girls being admitted as novice nuns?