I have 13 windows to fit. I won't be doing them all at the same time, likely over the course of 6 months. I plan to use Illbruck's i3 Sealing System (compriband, foam, tape). Can I buy all the gear now and will the compriband last that long (I read something about keeping it in the fridge, is that a thing?)?

It only needs refrigerating before you use it in warm weather.  If stored carefully it will last indefinitely.

I've half a roll in my shipping container that looks just the same as it did when I got it over a year ago.