お願いしてもいいですか? 　means "can I ask you a favor", "can you do me a favor", "I'd like you to do this. You can say this when you want to ask someone to do something for you. I think "お願いしてもいいですか? " is polite, but if you want to be really really polite, you could say "お願いしたいのですが、よろしいでしょうか？" You could say "お願いできる?", "お願いしてもいい?" to your friends.

Yes, this is a polite way to say "May I ask you something" or "May I ask you to do me a favor".....depends on the scene. You can say also お願いしてもよろしいですか？ It's more polite. But お願いしてもいいですか? is polite enough, so you don't worry in usual use. Also お願いできますか？　can be used in similar situation.