Gold Sending
Yes, you can send gold to any other players across servers using the mail system.
While I know it definitely works between EU servers I cannot guarantee you can send it from an EU server to a US one.
You should be able to. The Trading Post works across regions and you can send regular mail. I can’t see any reason they would block sending gold.
(Just be aware that if you regularly send or receive large amounts of money you might be flagged as a potential gold seller, so it’s best not to do it too often.)
“Life’s a journey, not a destination.”
Back when I was playing on an EU server, a friend from an US server sent me some gold via in-game mail to help with the transfer fee, but that was about a year ago. I see no reason why it shouldn’t be possible today.
As a warning, I did have a friend send another friend 100 GP which he had bought in the Anet cash/gem shot (birthday present), and get banned for gold trading. It was only a day or two, it was quickly straightened out since they could easily show everything was legit.
You can do it, unless if they changed it during the last 2 patches. As for the amount idk if there’s any limit or not.