Originally Posted by FlyerJosh

Here's the answers:

If you're cleared for the visual, the weather needs to be at least 1000'/3sm. Basic cloud clearances don't apply, but aircraft on the visual need to remain clear of the clouds in VMC conditions. As long as they aren't in clouds, they're good to go. Doesn't matter on the airspace.

If the visual approach is predicated on you seeing the airport (but not other traffic to follow), the controller retains responsibility for separation and wake turbulence. However if you accept a visual after reporting traffic to follow in sight, the pilot then accepts responsibility for the separation. (Reference AIM 5-4-21)