You can find ones which are more flexible, particularly for ones which do business in Australia. All the bank has to do is satisfy Know Your Customer, and they have wide liberty in picking how stringent they are on doing that. Citibank, for example, has an Australian operation. They have historically been good to people of my acquaintance in Japan. (A few years ago, they would accept a typed request on letterhead and a faxed copy of a Japanese passport as sufficient documentation to open a US account from Japan.)

Also, after you have a toehold in America, broadening it is much easier. One way to get a toehold is to, e.g., open an investment account at eTrade or another firm which also happens to run a bank, fund it, and then ask for a checking account. They'll typically satisfy KYC by means of "pre-existing customer relationship."

I have no direct experience with merchant accounts.

Most US banks are still operating in the 1960s. Everything needs to happen in person in a branch, or possibly for the more forward thinking ones, by mail. No email, no phone. Period. (Yes, you can call them on the phone, but you can't actually do anything.)

That means that you will have a severely painful experience opening a business account from overseas. I know this because I've done it, and it involved forwarding mail through a proxy in the US. As in, all mail from the bank went to a US address, where it was forwarded to me. Then I sent it either directly to the bank or back to my proxy in the US.

It hurt.

Every step of the way, they'll lose track of what they were doing and get small things wrong, which means you'll need to restart the process several times.

The only advice I can give is to avoid Chase at all costs. They used an entire month of my life before demonstrating that they were simply incapable of opening a bank account remotely. Key were a lot better, though still pretty painful.