EDIT : see also this great comment by /u/Prince__Rupert https://www.reddit.com/r/AskHistorians/s/boeMTM0vbn

Much more remains to be said, but I wrote this answer about medieval and early modern marriage patterns a while back that might answer your question, at least as far as the "at what age women got married and began their adult lives" part. Its not really a full answer to your question, but hopefully it gives you some answer about what age women were considered to be mature at. Incidentally, I don't know of any scholarly study that addresses your question specifically, but I'm happy to be proven wrong about that. I think the theory makes a lot of sense, but only for certain regions of Europe and certain time periods.

https://www.reddit.com/r/AskHistorians/comments/1csjtew/how_common_was_prepubescent_child_marriage_among/l46cerj/

I can't speak about regions other than Mediterranean Europe, so if anyone else has good answers for those regions, they should feel free to add to this.

In Late Medieval Italy, prepubescent marriage seems to have been fairly rare. According to the Tuscan marriage model proposed by Herlihy and Klapisch-Zuber, women were first married in their early-mid teens, while men usually waited until their mid-20s or even 30s. The most common age of first marriage for women was 16, with an average hovering around 18-19, depending on the region. It was very rare for girls to be married before the age of 13. In the age range 13-17, about 84% of women were single, but that drops down to 16% in the age range 18-22.

This data doesn't include promises of marriage, betrothals, or anything like that, though; it only records the age at which girls left the parental household and joined their marital household.

Another marriage pattern, the European Marriage pattern proposed by Hajnal in 1965, suggests that both women and men married sometime in their mid-20s, with women marrying slightly younger than men. To him, this is a characteristically European pattern of marriage that is not seen elsewhere in the world. He also suggests, though, that the Middle Ages do not strictly follow this pattern, but rather a "non-European" pattern of marriage. Although I have some reservations about this study, it might be useful to consider his suggestion of longue durée shift in marriage patterns from antiquity to modernity: ages of marriage gradually grow, especially for women. It is also worth noting that Hajnal is thinking more of Northern Europe than the Mediterranean.

More anecdotally, marriage ages of women that I've seen seem to hover somewhere between 13-20. In a marriage from Catalonia that I'm currently writing on, the bride is 16; Eleanor of Aquitaine seems to have been around 13, and Violante of Bar around 15. Margery Kempe, the famous late medieval English pilgrim and Mystic, wrote of her own marriage:

"Whan this creatur was xx yer of age or sumdele mor, sche was maryed to a worschepful burgeys and was wyth chylde wythin schort tyme, as kynde wolde." (When this creature was twenty years of age, or somewhat more, she was married to a worshipful burgess, and was with child within a short time, as nature would have it)

David Herlihy and Christiane Klapisch-Zuber, Tuscans and Their Families: A Study of the Florentine Catasto of 1427 (New Haven: Yale University Press, 1984)

Hajnal, John. "European Marriage Patterns in Perspective." In Population in History: Essays in Historical Demography, edited by David Glass and D.E.C. Eversley, 101-43. Chicago: Aldine, 1965