That is a tough list of requirements. The foreign exchange fee is probably going to be the tough one. The cards with the best rewards don't seem to offer very good deals in terms of interest and fees.

I would find a no foreign exchange Visa or MC (to avoid the Amex gap) for use in out of the country. Here is a fatwallet thread about it.

The Citi Platinum Amex might be a good choice for rewards on purhcases in USD - if you are OK with the Thank You Network. They have a deal going with 5 points gas/grocery and 3 points everywhere else. You can get value close to two cents per point on flight redemptions, so that is 6-10% possibly. It also comes with some of the protection you are looking for, along with a basic priorty pass lounge membership.

Your young credit history and mid 600s score might hurt you on some of the better cards though. Not sure where their cutoff is.