"Do I have to mail the original documents to you after sending the copies by fax?" You can use "Will I need to..?" if you want to sound a little more formal. The plural of "fax copy" is "fax copies". "Alternately, I can submit the original documents when I arrive in the USA." It just sounded like a broken thought when you started the sentence with "or". Would you consider writing the sentences as one question? "Will I need to mail the original documents to you after sending the copies by fax, or can I submit the original documents when I arrive in the USA?"

Do I have to mail the original documents to you after sending fax copies or can I submit the original documents when I arrive in the USA. Just those two small things, everything else was good.

Should I mail the original documents to you after sending faxed copies, or can I submit the original documents when I arrive in U.S.A?

Very understandable but not quite right. How about: Do I have/need to mail the original documents to you after sending faxed copies, or can I submit them after I arrive in the USA? Welcome!

Closely correct, yet here are "better" ways (and more grammatically correct) of writing those two sentences. First one: Do I have to mail the original documents to you after sending the faxed copies? Second one: Or can I submit the original documents when I arrive to the U.S?