I was terminated from my job as a restaurant manager by the owner of the company. I was at work on a Tuesday and he asked me outside and said" It's not working out and I want you to resign" I said no and asked what the problem was, he said" I don't want to get into it" My final check paid me for 1 week and a day. I am a saleried manager and wonder how he could cut my second week up.
The more important question I want to know about is if it's OK to do a backround and credit check without my authorization. He told me of this after I had been on the job for a month or so. He also told me that he needed to get me to sign an authorization form for him. I never signed anything to that effect and was afraid to find out if it is illegal because he would fire me.

You are never legally entitled to be paid past your last day worked. The definition of "salary basis" includes an exception for the initial and terminal weeks of employment.

Background and credit checks are not my area of expertise. But, since you're no longer working there, I'm wondering what you're considering doing even IF your authorization was required. You can't be discharged twice.

He is not legally obligated to pay you for any time beyond the last day you actually worked.

Whether he can do a background check without your authorization depends on whether HE is doing it or having a third party do it.