Do all European bank cards have the associated bank account number printed on them? Mine has, the full IBAN.
Also, I found out when I began working for international clients, the U.S. doesn't participate in the IBAN system. Instead we have something else which necessitates international wire transfer payments be made via an account number, a routing number, and a swift number. It's very annoying. (perhaps business accounts work differently, I get paid directly into my personal account which I'm sure is a bad idea, but it works for me).
No it is, almost all my purchases are via debit but it comes off my credit card. Most banks come with Credit cards that are just a fee-less low-liability proxy for debit that gets withdrawn from the bank account.