Do I have to print and mail a copy of my federal return with my payment? It was already e-filed and accepted.

If you e-filed you do not need to send in any documents, unless instructed to do so (for instance: you will need to send in your 1040-V payment voucher only).

You can pay your Federal balance with your bank account for free, check or choose an approved payment processor to pay by credit or debit card. You can also setup payment installments. 

Here's a link to the IRS website for making electronic payments: https://www.irs.gov/payments