E-filing cant put my SSN on it. Can I still use my father's account?
You mail a check to pay tax. Do you mean to direct debit it? If so then the IRS won't care but the bank probably will. Many banks do not allow either direct deposit or direct debit if the name on the account does not match the name on the transaction and will deny it. Check with the bank to see if they allow that.
That would be up to your father. The IRS does not care who writes the check but your SSN needs to be in the memo box on the check so that it gets credited to you.