1. What does "sleep tight!" mean? and is it common? It means 'I hope that you sleep well'. It's an intimate thing to say, to a friend or loved one. A little less intimate is 'Sleep well'.
2. What does "come on in" mean? and is it polite to say? It's just a slightly more informal way of saying 'Come in'.
I thought as much that it has an intimate connotation thanks a lot it's not like I had learned from anubod really it was just an inside knowing that when I hear someone especially ladies say good night Sleep tight