Best way to Submit 2021 Federal Amended 1040X

I did my 2021 federal Amended 1040X Tax Return on 2/25/2022. When it comes time to print the Amended federal 1040x, it also printed my 1040 unsigned. On my 2021 Federal 1040 I got a refund. Now on the Federal 1040X I owe. Turbo Tax instruction page say to mail return (I assume everything that printed for federal tax return only and mail to irs with a check) When I continue it is allowing me to file the amended federal return. It also gave me a website to use to pay the taxes I owe. www.irs.goc/payment

 

If I mail the return and payment, do I sign and date both the 1040X and 1040 that I previously submitted? 

If I file online, do I have to mail any return to the IRS?   Would I just mail them a check, or do I use that web site to pay what I owe by credit card? If I pay by credit card would this be treated as a purchase or cash advance transaction by the credit card company?