Wrong section, but IAH will not give you any trouble as it is far from the border. And no, when you change planes, you're in a secure area and don't leave it so no need to show ID.

I don't know about United, but I remember Continental being pretty good and knew a few of their flight attendants (they tend to be on the naughty side let's just say). They were not thrilled about the merger with United but overall, it's a respected airline...I think you gotta pay for bags though. So no worries and go fly the friendly skies.