Go to where i am in the picture everyday and talk to her, you'll find erotic books and she will read them with you. Eventually, she will start asking questions about the things in the books and start doing them with you.
This is, indeed, the way to unlock new positions and options. Unfortunately there's a good deal of RNG involved. You have a chance to:
A) Find nothing.
B) Find a generic book that just gets her horny.
C) Find a book that teaches her a new position.
Of course 'C' is the least common one. I actually tend to get 'B' the most. I've unlocked handjob, blowjob, licking, and cowgirl. I'm not sure how many options there are all together.
As for anal sex: keep licking and fingering her ass until you can get your fingers inside. Then have vaginal sex with her to lube yourself up and then you can do anal sex. It can take a long while before you're able to insert it. I'm not sure if doing repeated anal sex helps to permanently loosen her up or not; so far it doesn't seem to for me.
Lastly:
1) Do you ever get to change her outer clothes (i.e. not just her underwear and hair clip)? Or is the developer saving that for DLC.
2) When do you start unlocking actual sex toys? I'm on day 35 yet outside of the injections and drinks I haven't seen anything.
3) Is there any point in messing with her urethra? Maybe I'm just underestimating the game but I doubt you can insert your dick into it, yet it does have an 'expansion' stat. EDIT: Never mind, you can fuck her there.