No. It can happen anytime.
Primal Groudon's Desolate Land create a stronger Harsh Sunlight. With Desolate Land water moves don't work at all.
Vulpix, Ninetails, Groudon, Torkoal and Mega-Charizard Y are the only ones who can have that ability
Drought is the only one
Drought would be the ability that brings the sunny day abilities, but Groudon in particular can Mega Evolve via the Red Orb and cause the drought to become heavier. All water type moves are then unusable from that point on.
No their are other abilities
No, groudons ability...
I think so. The only other way I know that causes sun is sunny day...