Ok seems you're right about the cooldown on the books... Perhaps it's a week or something? Don't recall exactly how long it was since I used the gifted book and bought the new ones but it let me use one just now.Stat growth options has a certain limit roughly 30, after that you can train it directly.
The dance as club, gym and school are the only reliable increases after the threshold, that and the occasional haircut that apparently are weekly.
Also the stat books has a cooldown like the items, haven't figured out what's the length thou.
The issue with not being able to give gifts remains an issue for me though. Can't think of a reason why I wouldn't be able to. Can't recall when it disappeared as my saves have been relatively far apart which makes it tough to track down exactly when. The only thing that comes to mind (though likely unrelated) was I learned the massage skill and I see the icon there for some girls where the gift icon used to be.