The question banks are not identical, although many of the questions based on the regulatoins are pretty similair. There are many question on the FIA written (flight instructor airplane) that are not in the commercial bank. For instance, the FIA will ask you questions about giving student pilots endorsements, student pilot eligibility requirements, recreational pilot requirements, etc.
I would not reccomend that you take the FIA unless you buy a study guide and go through it first. Just using the commercial guide will probably not be enough to pass the FIA with a score above an 80. I probably would've failed the FIA if I tried to take it without studying.
The FIA and the AGI (advanced ground instructor) should be taken at the same time. The AGI is identical to the FIA, except for that the fact that it has a dozen or two additional question about ground instructor currency in its pool.
The AIF (flight instructor instrument airplane) and IGI (instrument ground instructor) should also be taken at the same time.