What is the typical angle of attack aircraft fly at and at what angle of attack do they stall?
It depends basically on the wing section. Some of them stall at a higher angle of attack than others...

To quote typical values (for wing + body, since not only the wing gives lift...) a given plane may achieve the flattest glide (best range, L/D = 12, at 155 knots) with an angle of attack of 4º. If you wish to fly slower, you can do it at 115 knots, with L/D = 8, and a steeper AoA (13º) or you can choose to fly faster, at 210 knots, always with L/D = 8, but with an AoA of 1.5º.



Thus, and except for the best L/D, there are always two angles of attack for the same L/D, one of them steep (slower flight) or flat (fast flight)...

The stall, for the example I'm quoting (book 'Mechanics of Flight, by A.C. Kermode)' takes place at 15º...