As long as you have a job & good credit.
Depends on who is lending you the money. Most dealers will not, but your bank or credit union might if you have good credit and history with them. If buying for a family member, then great, but if for yourself, then wait till you have your license back before purchasing a vehicle so you can drive it legally.
What happened to your license?
Yes you can. Here in the U.S you don't need a drivers license to buy a car all you need is legal ID. If you drive the car then driver license is a must.