when you sign a contract at an auto dealership, can they back ou on it if they cant get financing on that deal

Answer 1

Yes the contract is contingent upon them getting financing for you.

Answer 2

Yes, they can. They can say they couldn't get financing at the advertised rate, but then they say they can get it at like 22%. When you go in, first, go to your bank and get approved for a loan, so then they can't say you couldn't get approved at a favorable rate. If they try, pull out your bank papers and say, "Bull". Then pick the papers up and walk.
NEVER sign over your tradein until you have approval on the financing! Once you do, you're pretty much committed to whatever deal they want to shove up your a**.
They will try to insist that you sign off on your tradein, and give you a lot of bull about how you may as well take care of this NOW, while you're filling out the application for the loan. Look them in the eye and say, "I've got nothing but time this week. I will wait until my loan goes through at a favorable rate. If it doesn't, I'll purchase my car elsewhere." Let nothing sway you from that position. Take it from me. I made all of the mistakes I warned you about and wound up with a VW Passat. What a lemon. Should have been yellow with green flecks all over it. I wound up paying 22% for five years on the Passat, which means I paid more than twice what they charged me for the car! I learn by my mistakes. I hope you can benefit from the expensive and stressful lessons I learned.
Best wishes.