Reported speech

Can somebody please tell me when I should backshift and when I should just leave it as it is? I've tried looking it up in my grammar book but there were no rules that I could find anywhere that said anything about when not to backshift. Here are some examples I'm not sure about:
I heard you are/were hiring.
I told you I will/ would be moving next saturday. (Haven't moved yet)
He said he didn't/doesn't like apples.