About your point 2, all airfoils have an angle attack at which they generate no lift at any airspeed. As I said, there's nothing magic about a flat bottom (other than being really easy to build on both the wing and fuse side of things). With most flat bottom airfoils, the AOA for 0 lift is going to be several degrees negative, maybe -3 or so, dependingon the exact airfoil of course.

Also, remember that AOA is measured from the center of the LE to the center of the TE. A flat bottom airfoil set up so that the flat bottom is at 0 degrees is actually sitting about 1-3 degrees possitive AOA. So when you build a plane with a flat bottom airfoil, and put that wing saddle at 0 in relation to the horizontal stab, you're really building in a few degrees of possitive incidence.

What is true is that the more camber you have, the more lift you generate at a given airspeed and AOA (within reason, and with plenty of exceptions). Since a flat bottom airfoil has a fair bit of camber, you get an airfoil with pretty good lift. Combined with a straight wing, lots of wing area, and a fairly thick airfoil, you get some gentle handling properties. But it's not all about the flat bottom, that's all I'm saying.

However, most all of the really good basic trainers DO have a flat bottom airfoils. Some of the reason for this is historical and some is marketing.