Slawa

As far as I know (30+ years of invoicing clients) there are no absolute requirements for an invoice in the US. As long as it includes
your name and contact information,
your client's name and contact information,
the date,
invoice &/or purchase order number,
description of work and amount requested
any restrictions or caveats (e.g., payment is due in 30 days; work won't be released until payment is made in full, etc.)

you should be okay.

But 2 things you should be aware of:

1) there is no national sales tax equivalent to the VAT. As a foreign entity, you may or may not be required to collect state sales tax on behalf the state where your clients live. Check with a business liaison officer at the US consulate or embassy--they should be able to show you how to find out.

2) the US checking/payment system is "backward" from that in Germany. When, in the US, you send a bill to a client, they cut a check and send it to you. You then deposit it in your account. So there is no need to give clients your bank account information.

Of course, this will make no difference if you're relying on an automated withdrawal system or an automatic payment on a credit card or PayPal account.