I received a 1099 M for work that I hired a contractor to do. Can I send that contractor a 1099 M to offset the income I made? I am not set up as a business. If so would I use my ss# where tax id# is asked for?

Yes, if you paid $600 or more to a contractor, you must issue 1099-misc. Also you have IRS reporting requirement. You can get forms at office supply shops.

Yes, use your name and SSN.