I think I’ve seen the movie two times, but I’ve read the book a few more, so I’m pretty sure these answers are generally correct and could be applied to either the book or the movie.
Don’t these vampires have healing powers? Yes, they do, but the powers are relative to the “age” of the vampire (how long it has been since they became a vampire,) and the severity of the damage. During the events of Interview, Lestat is rather old but a comparative spring chicken compared to some of the vampires we meet later on in the series. So Lestat, a relatively young vampire with extensive injury is going to take a long time to heal. His resulting weakness is, I believe, what prevents him from killing a human. Rats are about all he can manage. Yes, human blood is the best, and he would get it if he could.
Claudia. Yeah. She always has the body of a child even though years and years go by, which is a source of frustration to her. In the Anne Rice vampire mythology, there is a sexual aspect to the relationship between vampires and the vampires they create. However, if memory serves (I gave up on this series after the 4th book, I think), they are not actually having sexual intercourse in the way that human beings have sex (unlike some other modern vampire stories, like the Anita Blake books or the Buffy series, where they vampires both drink blood and are up for a roll in the hay). For Rice, the sexual release comes from the shared drinking of blood. It’s a really drawn out metaphor, and, IMHO, gets pretty tired fairly quickly.