There is no real difference between these phrases, But you can say "I don't know him", and (for obvious reasons) you can't say "I have no idea him". I do think "I don't know" sounds more polite, depending on the context of course. "I have no idea" can sound dismissive. For example, when asked for directions, I will often reply "Sorry, I don't know". But that's more about personal preference. :)

I agree with what others have said. "I have no idea" sounds pretty final and if used in a sentence such as "I have no idea what you're talking about" the speaker can sound exasperated or defensive depending on the context. I once asked a cashier at McDonald's how many oz. were in a snack-sized product and she said "I have no idea." Nothing else. An apppriate response would have been "I don't know, but I'll try to find out for you." I would say very seldom should "I have no idea" be used on the job.

Hello dear. There are many ways to say the same thing! Example: I'm lost / I'm foxed / I'm puzzled = I'm confused.

No difference. Use which ever one you like, but it's more common to hear people say 'I don't know'.