No need to remove the regulator. The motor just unbolts and unplugs.
No grounding. The motors are fed positive and ground through the two wires. The polarity of the wires changes in the switch, simply reversing polarity for up or down.
Yes, the white piece on the back of the switch unplugs from the switch. As mentioned, they can be rebuilt and
@Devinism is your go-to for this.
Which door is it on? For 3 of the windows, you have the master switch on the drivers door and the switch on the door itself. Does it behave the same with both switches? (forget that if it's the drivers door)
It's my experience though that the biggest problem is the commutator in the motor just gets dirty and the brushes don't make good contact. The motors aren't too hard to pull apart and clean. Here's how I did mine.
Power Window Motor Repair