Is there some way to change the co-signer on my car?

That is something that only the lender can give you permission to do, so contact them. If you have someone else who would meet the criteria for cosigning, they should have little problem allowing it.

"Co-signer" means the person who agreed to pay the loan if you don't. If that is what you mean and don't mean co-owner, then you would have to ask your lender but I doubt they would allow it.
If you mean "co-owner", then both 'owners' would have to sign to remove one owner.

Yes. You have to pay off the loan first. When someone agrees to co-sign a loan, they are the co-signer until the loan is paid in full. The lender is not going to change co-signers while a loan is open.