A few. It is not in any way a major focus of the game, so if that's what you're after, you may be disappointed. There are a couple of incidental male characters the MC can have sex with, but the vast majority is m/f content.
I have no special knowledge, but considering that they are already fully corrupted and under the MC's thumb (to the extent of worshipping him, willingly engaging in threesomes with each other, etc.), I wouldn't expect any major progression with them until the endgame or if/when new training paths are added: There just isn't that many ways for their story to progress apart from that. There have been a few scenes added here and there, but no massive expansions of their content.
From the latest ChangeLog: There is a bug in a journal somewhere, which says that you need to continue corrupting the university when the task is done; this has not been fixed yet (need to look further), but it should't stop or affect the main story AFAIK
You can buy Supplies while at home (at least I can) and then go to the Lab during the day where you have to option to make serums. If you do not alreay have it, the Walkthrough on the OP is a good start even though it does not go all the way.
As long as it is avoidable you can have all the fun in the world.
I do not remember any blatant scenes of the women going around having sex with all the guys... however, keep in mind you do run a bar/brothel. You are expected to gather intel and part of the women's jobs is to assist with that. Sex is one way to get that intel. So, you may want to consider making some of them Public Use to not lose those opportunities!
Well, as the game stands now (so it may change) I don't see a real need for making the girls public mechanics wise, less so if you want to keep them to yourself. Storywise you already have four employees and intel is gathering up faster than you can use it anyway, similar to the other resources. And while not many, there are some scenes where they will do things in public (mom telling stories, boss and the delivery guy on fridays).
