Is My Sisier's Keeper an appropriate book for a 13-year-old?

Sure it is. I know fourteen year olds who have read it and liked it just fine. Of course, it all depends on the kid - there are some...explicit, shall we say, parts of the story, but honestly, by the time they are thirteen, most kids have seen worse on TV, and heard way worse in the dirty jokes that middle/high schoolers just adore. The topic is fairly serious, but nothing the average thirteen-year-old couldn't handle. The big problem with the book, I thought, is that a lot of the parts where Kate is sick in the middle are just gross. Really gross. Lots of blood, and what not. Also, there is an arsonist in the book, and a major character dies at the end. The end isn't what I'd call happy, either. There is no reason why a thirteen-year-old couldn't read this book. There are probably a bunch of kids who just wouldn't be into it, but that is true of any age. Thirteen year olds aren't really children any more, they are small and inexperienced adults and (the majority at least) can handle the subject matter. Hope I've answered your question!