As you said, there's no mention of this in the books. But we can speculate.
Let's look at each of your questions:
- How do they learn about puberty?
In all likelihood, they learn from their parents. Most Muggles also learn from "The Talk;" kids at Hogwarts can do this just like kids at Muggle boarding schools. What really happens, though, is that they learn from older kids. Ron, for example, probably knew all about this from his brothers, and Ginny from her mother (and to a lesser extent her brothers) but kids probably learn most of it from other kids. This is why Harry knows like nothing about it--his parents are dead and his uncle and aunt would never do this service to him. It's also possible that Madam Pomfrey teaches a health class that we never see, like Madam Hooch's quid ditch class that we see only once.
- How do they learn proper bodily care, especially girls?
It's possible, as I said, that there's some kind of class from Madam Pomfrey which goes into detail about proper care of the body. In addition, asking a professor (although way up on the awkward levels) is possible. Parents probably include this in the Talk, and older siblings and/or housemates might provide advice. For girls--some of them will begin their periods at home, but the rest probably just have to go to Madam Pomfrey and get something for their needs (sorry if I don't know much about this, since I don't have them).
- When do they get haircuts?
This is hard. Obviously they do get haircuts, but it's unclear how this could happen at Hogwarts. The only mention of haircuts in the series I can think of is this:
It provided a distraction, watching Mrs. Weasley force Charlie into a chair, raise her wand threateningly, and announce that he was about to get a proper haircut.
A short time later he has "brutally short hair." Obviously haircuts are easily done and given with wands. I can thing of a few ways they can happen at Hogwarts:
- Madam Pomfrey cuts students' hair. This would be easy for her and would take like no time
- Other teachers run some kind of service every few weeks or so for money. This explains why the Weaslys have so short hair
- Other students cut hair for money.
- Students cut their own hair. Easy and short
- Runs into town. When I went to a camp--not a boarding school, but 6 weeks long--kids would take walks into the nearby town to get their haircut. Unfortunately, this would not be available to students in 1st or 2nd years.