The lemon detox diet is a really great and popular new fad amongst America. It helps the process to speed up metabolism and also promotes detoxing the body at the same time. You can find recipes and guides here: www.lemondetoxdiet.com.
No, it's not possible to speed up the process of puberty. Just ensure that you're eating enough and are as healthy as possible, and it'll start. It's a natural process that you shouldn't try and speed up at all.