You may find that they become friendlier and more accepting of being touched once they start laying. I try to respect my chickens' wishes and not touch the ones that don't like it unless necessary for their health.
Squatting is what they do to show their readiness to mate. When you massage their back, they give a little shake of their feathers just like they do after mating. I think they equate being touched in that way with mating.
Yes.
I think that without a rooster in the flock they are happier with me acting as their rooster. I can't prove it, but frustrated instinct in animals often results in undesirable displacement behaviors.
My cockerel is 17 weeks so soon he will be able to step up into his natural role.