2. Ask if they have a Taxpayer Identification Number and what it is. Everybody needs either a Social Security Number or a T.I.N to open a bank account....
Probably you won;t have to get through 2 through 4; #1 should be enough to send the scammers/flippers packing.
I'm glad you said what you did after, because giving out your social security number is like giving out an open invitation to get yourself ripped off. 73!