Yea, asking to meet her parents was a little on the quick side, but a mistake is a mistake and you'll learn. Whatever you do, don't apologize for everything just move forward. If she's into you, she'll be willing to forgive you even when you do something a little strange.
Also, you let her know that you like her already, you don't have to tell her again until she reciprocates it somehow. You can drive girls crazy by constantly professing your feelings for them, sometimes you just have to give a litttle space.
The book borrowing thing is great, let her borrow something (not everything you own). If you become part of her hobbies (like manga for instance) you'll have a much better chance at being accepted.