Would I be able to buy and fix a 1967 Chevy Impala for under 10,000 dollars? If not, how much?

Be serious. That car is 50 years old. You are going to have to completely disassemble it and test every piece to be sure it is still usable. If you have to replace something there is a good chance you will need to hire a machinist to custom make it. Multiply your budget by 5 and even that is a low estimate.