I just purchased a car... I think!?

I just purchased a car, I think. I signed all paperwork (purchase terms, gap, title, etc --- told my interest rate, told who my lender is, when the 1st payment would be due) and wrote a check for $1,500 and afterwards requested copies of each item I signed and the finance officer told me because I am special finance I do not get copies... the lender will mail all copies to me. I never heard of this but I don't know what to do. So I left the dealership with the car, proof of insurance, a buyer's tag receipt, and an automobile loan receipt with a return date of 07-08-11 @ 4 PM. Is this the normal? Will I have to return this car? If yes, will I be able to get my deposit back? Do I really have a car?