Mob Rule can affect creatures you already control or ones that are already untapped. It will untap them if applicable and give them haste.

You choose which mode you're using as you cast Mob Rule. Once it's cast, you can't change its mode, even if creatures' powers change in response.

Gaining control of a creature doesn't cause you to gain control of any Auras or Equipment attached to it.

Once you gain control of a creature, it doesn't matter what happens to its power.