Will I need physical therapy if I tore a ligament in my thumb?

Yes. Depending on the severity of the tear, the treatment will either be conservative with a period of immobilization in a splint or a cast followed by mobilization exercises usually conducted with a hand therapist occupational therapist or surgery, immobilization for a period of weeks depending on the surgeon's orders and then work with a hand therapist.
Depends. Depends more on your symptoms and whether you have any functional deficits. If so, seeing an occupational therapist would be a good place to start.
Yes. Torn ligaments often require immobilization for weeks. Some require surgery. You will benefit from physical therapy to restore full range of motion and strength to the thumb joint once it is healed.