what is the international center for dispute resolution (icdr) and does it have anything to do with the american arbitration association (aaa)?

The ICDR is the international arm of the AAA and administers all of its international arbitrations. You can use the ICDR to arbitate your dispute no matter where in the world it happened.

are the aaa or icdr biased in favor of american parties or is the organization a part of the united states government?

The answer is "no" to both questions. Both the AAA and ICDR are neutral private organizations that are impartial. The ICDR administers arbitrations held under its arbitration rules for parties of all kind of nationalities around the world.

does choosing the icdr or aaa mean that united states law determines how my icdr arbitration will be conducted?

No, the arbitration will be conducted in accordance with the AAA arbitration rules the parties included in their contract and with whatever other law that was selected.