Nat sounds like gnat, so I wouldn't use it as a nickname. Maybe just if you're calling them or something, but not as a name they'd be called normally or write down on their paper at school. I think it sounds more like a girl's nickname (like for Natalie). For a boy named Nathan, I'd use Nate for a nn.
None of those names are my style, but I think Nahar is the nicest.