No, you don't need to open up corporation or LLC. You can driver truck as a sole proprieter. Having a corporation or LLC, do provide peace of mind, since you are not fully liable for any loses caused by operation of your business.

Yes.

Given that you already have your CLD and truck purchased, it takes about 25-30 days to complete all requried paperwork.

Yes, as long as lease agreement is signed by both parties. Both parties include, person who owns the DOT and person who will lease the DOT.