hi Max,
welcome to Zurich! Christopher Street day is coming up - a big deal in Zurich (
http://www.csdzurich.ch). In past years, events have been a combination of political activism and pageantry - something for everyone. I understand Berlin's mayor, who is openly gay, will speak this year.
also, check out
http://www.zuerigay.ch/en/index.php
as for cafes and bars, there is a cafe across the street from the Zentralbibliothek in Zurich which used to be a favorite with the gay community - not sure if that's still the case.