I think that only applies to EU citizens. I know last time I was delayed in a European airport only EU citizens got the compensation. But maybe worth double checking.
Huh, I can't find any explicit information confirming or invalidating your statement. However, I got my direction / non-EU airline info backwards. If you are flying on a non-EU airline into the EU you are out of luck. However, what matters is who is actually operating the flight. If AA sold you a ticket for British Airways or Finnair you're still flying on an EU airline.
There are also plenty of websites that will deal with your claim with no risk for you, but will grab 25% of the compensation + VAT in exchange.