After a return has been efiled and accepted, it can sometimes take a return PDF a while to update and become available at the Tax Home. If you can't use the Download/print button at the Tax Home or the "Download/print the PDF" link in the section "Your Tax Returns & Documents", or if you're getting incomplete documents when you use one of those methods, here's an alternate way to print by opening the filed return back up to print at the Print Center.
NOTE: When you open your return back up, do not make any changes in it if it's already been filed. If you later have to amend the return, it has to start off exactly as it was when it was originally filed.
NOTE: Remember all PDF tax documents and tax data files are very sensitive files, since they contain your personal ID info, financial data, and possibly bank account numbers, etc. Be sure to store them safely and securely to guard against computer theft, hacking, etc.
As to the form of submitting this information, copies of your own tax returns are acceptable, but the immigration officials know that it wouldn't take much for someone to forge these.
Therefore, they prefer to receive tax transcripts, which are generated by the IRS and show detailed information of your tax filings. The IRS offers a free online portal at which you can download and print your tax transcript immediately. Go to its "Get Transcript." page.