if that unit is 8 years old like you say, it has 2 stepper motors (chokes) take off the air filter cover and make sure the choke plates move when motor tries to crank over. Usually it first closes fully then opens 1/2 way. it may cycle a few times. . Also, there's a small stepper motor in there

and a spring that moves the choke plate over the venturi when cranking. These little motors have been known to freeze up or rust. Theres a second round stepper motor

on the side of the air intake box that should cycle during starting also.
if both of these are working properly, then its either spark issue ( i use an inline spark tester) or fuel delivery. if all else fails, you can take a blunt object like the back end of a drill bit and push on the fuel bellow inside the fuel regulator down by the battery. there are 4 or 5 holes on face of regulator.

while cranking and not starting if you gently push object into one of these holes and unit fires up, you need to replace regulator.
ive never seen mice problems in any generac unit ive worked on. they have a good metal screening system. Changing the mags is not too difficult, but i have not seen that issue too often. you HAVE to verify spark first. You have not stated whether she has had the valves adjusted in the past. i have brought dead generators back to life many times with a simple valve adjustment.
as for propane starting in severe cold, the only issue i've ever seen with this is in the propane tank itself if allowed to get too low, or a tank thats too small. Ive had some people try and run a generator from a 100 gallon propane tank. ive had several issues with this. i even had one guy try and run his with a bunch if 7 gallon tanks. now these will freeze up. I've had mine running when its 10 below and never had any issues . At that time i had a 500 gal above ground tank. Now i have a 1,000 gal underground tank.