It's great to see another cyclist has joined the Forum

. I can't answer your questions directly, but I can point you towards places where you may find the answers.
Two other threads about English-speaking cycling clubs in Zurich:
Competitive cycling in Zurich [Zurich Area] English-speaking cyclists
Also, as dakman said, get yourself along to the Thursday evening rides organized through EnglishForum (e.g.,
fifth thursday night bike ride).
I don't know of any crit races, but there are several cyclosportifs, most of which use quite mountainous routes. Here is the thread:
Bicycling: long-distance, mass-participation rides. Plus, I made an index of all the rides on
this website.
You should certainly check out the extensive
Cycling in Switzerland thread, there's lots of info there that should answer many questions you have about riding here.
Bike mechanics near Zurich have been discussed
here and
here.
All the best with the riding!