I don't know about the FBI, but in the Border Patrol we got 6, and I think it was mainly for training purposes and to have spares.
The academies have to have pretty efficient use of time in order to get agents out into the field as quickly and cheaply as possible, so class A gets the range for a 2 hour block and then class B gets the next 2 hour block.
You load mags while the instructors go over the teaching points for the day, and then you go shoot through 6 mags worth doing drills and such.
Then you reload all 6 mags while the instructor goes over the next drills. It's a pretty efficient way of doing things and seems to work well. You could argue for 5 mags or 7 mags I guess.
Most folks carried 2 spares on their belt and 2 more in the car/camelback, but some guys did carry 4 spares on the belt. I never saw anyone carry more than 4 spare mags.
I'm not sure, but I think so. I got to proofread an item request form at one point for night vision stuff, and the specs for the item we were requesting were basically copied off of one manufacturer's website for one of their models, but anyone was theoretically able to offer the product at their lowest price point. I think you nailed it with "just a gov't thing."