You shouldn't ever really tell someone it's their turn to talk, but in an organised or rehearsed context, or in the newsroom for example, would be fine - over to you...

Used in meetings when you are changing speakers or presenters. Its not used in conversation.

As the others have said, it's mostly for presentations. It's not really for telling the other person it's their turn to talk -- mostly, the purpose of it is to tell the audience that you're done speaking, and someone else will speak now. It makes the transition between speakers a bit more smooth.

It would be "hand it over to you" or "turn it over to you". You need to have the word "it" in the sentence. "Throw it back to you" would only be used if the person you are giving it to had spoke previously.

I would only say that in a presentation at work or school, but I guess it can be used in other contexts, too?