Let me start at the end. Indeed, the attractive forces between atoms may make it harder to lift an object. The actual reason is adhesion or cohesion – if the surfaces are "sticky", it's hard to separate them.
Adhesion is only counted in friction if we study the effect of the adhesion on the sliding motion when the surfaces remain in contact. If the surfaces are separated, the adhesion obviously stops acting as soon as the surfaces are separated. So this part of the "friction" immediately drops to zero.
To answer the remaining two questions, the "clashes between the peaks" rather than "adhesion" is the key to understand the right explanation. Imagine the two surfaces as cogwheels.
The friction arises because the teeth have to jump out from the holes on the other surface which requires one to move the object perpendicularly to the surface and perhaps break some of the teeth. Work has to be done for these events to occur which means that some extra force has to be exerted for the surfaces to move relatively to one another (to slide).
Why is the kinetic friction smaller? Because when the surfaces are already moving, the "teeth" of the cogwheel are no longer sitting in the "holes" of the other surface – they have already been lifted from the holes. The surfaces have been separated – by a distance comparable to the "depth of the typical holes". While the peaks may still "drop" to some of the holes on the other surface, they don't drop as deeply as when the surfaces were at rest. So the "lifting" one has to make is smaller than it was at rest, and so is the corresponding friction force.