www.faa.gov is the faa website. FSDOs are now closed to the walk in public - at least the DAL one is. You just have to make an appointment first.
Not sure what the A4 (They call it eight and a half by eleven) was that you got. I doubt it was a form 8710 (that's the license application form) and it could have been a print out of your records, except that you won't have anything to print
So it must be what the other bloke said: a letter that allows you to get the US license based on licenses earned in a foreign country.
Where are you going to do your timebuilding?