Yes they are and you should form a simply company to protect your assets in the event of an accident, even if you have insurance. It is cheap to do

Yes, they are.

If I buy my own truck to work as an owner operator do I get my license plates through the company I'm leased to or do I register the truck myself? Also do I have to get a USDOT number and display it in my truck? And last I believe that the motor carrier name is supposed to be displayed on the they I as well is the motor carrier me or is it the company I'm leased to?