Babyblade: Verification of FAA License can be acquired from FAA website under Airmen certification - Verification of Airmen Certificate.Shoot them an email with required information and they will Fax/email you the copy of it.
For verification of Flying Institute contact your CFI and they will email you a copy of Air Agency Certificate issued to them by FAA.
As for the medical I have no Idea as I didn't submit that, But you can contact FAA and they will be able to help you with that.
