Not complicated at all. The answer is yes and yes. It's not a reg, it's in
https://www.faa.gov/documentLibrary/...der8080.6d.pdf
At least you don't have to take the full tests. They're only 25 and 20 question add on tests.
I'll just say as a CFI you don't have to know everything but the FAA puts everything on line. You should spend some time lurking around the airman certification section on FSIMS.faa.gov. Sort of get to know your enemy.