Try the phone numbers on this link:
The website does not give rates, or at least I could not find them. I have not flown into Innsbruck yet, but fees on other Austrian airports were: Salzburg: EUR 25,51, Graz: EUR 22,50, both cases on a Diamond Katana. So I guess, Innsbruck will be about the same.
Let us know how the approach was, Innsbruck looks quite demanding, judging from the approach plates. And watch out for Foehn winds! If you need help, let me know, I know a bunch of people who landed in Innsbruck.
I am totally missing basics and clueless about airline flying!