What causes the adverse pressure gradient that leads to flow separation?
Friction plus pressure rise.

No, the effect certainly isn't independent of surface friction, otherwise the location and angle of attack of separation wouldn't change with Reynolds number.

First, friction will prevent the surface layer to become as fast as the outer flow in the suction peak, and once pressure rises, all air will slow down by the same amount. Now the already slower part near the wall will actually reverse because it slows down to a standstill and is attracted by the low pressure ahead.

Pressure has to rise past the suction peak in order for the air to get back to ambient pressure. The upper side suction is caused by the airfoil's curvature, and curvature  over the rear part of the airfoil is very low or even negative - that is what makes the air assume ambient pressure again.

I think you know already my slightly longer answer on that topic, but I will link to it nevertheless. Please let me know if I need to explain more!