So which method or type of filler should I use for this side view mirror base?
Material: PA Polyamide (Nylon) plastic.

 

I think I would try to weld in a patch rather than use any filler for that whole area. Though, if you do need some filler, 3M Automix is great on plastic.

 

if the front part (part facing out in the pic) is flat enough to make a decent seal

i would use a piece of glass, heavily waxed (several coats) as if you were waxing the inside of a mold, lay the mirror base down, use a 2 part epoxy for plastics and fill it up

sometimes thats just a pain in the ***, im lazy, i would use 2inch tape and tape it off instead of using the glass

 

Go to an autobody store and read the back of the cans. It will tell you
I would personally use duramix