For the most part, I think it's probably a no for me. But when I'm babysitting and I decide to take a nap, then it's a yes. I don't allow myself into a deep sleep during those times and I have my ears keep an 'eye on things' while I get a little bit of rest.
Maybe...? Very familiar noises don't seem to wake me. Noises that my brain says, "What's that!?" often do. So maybe it depends on the sound, the stage of sleep, and whether the noise is something my brains thinks I should pay attention to.
Yes and it influences my dreams a lot too. It's really funny when a regular sound suddenly completely changes the course of my dream. I like being able to be aware of what's going on when I'm sleeping though.