I've found the fiberglass is ally easy to cut. Many types of tools will do the job just fine. For a slow and calculated/accurate cut I've found the oscillating tools work very well- I have a Drexel multimax. Just make sure to carefully mark out the new cuts, I prefer blue/green painters tape as it give you a nice defined edge compared to a pencil line, plus if protects the surrounding fiberglass should your cutting edge slip a little. I run a shop vac directly under the path of the falling fiberglass dust, and wear proper clothing and lung/eye protection.
Check out this Maxxair fan I found one for significantly cheaper than in this link.....
Mine only drops below the interior of the ceiling by about 3/4" and I did not have to build up a structure above the roofline. I only had to create a thin 1/2" spacer for the interior perimeter of the mounting flange. I'm super happy with the fan so far, it can stay open in the rain with its integrated vent/cover. It has something like 10 speed settings or so.