Innsbruck is a sick city to live in, tons of stuff to do winter and summer.
Most people here speak English, especially with the younger generation it's not a problem, and a little bit of German will get you a long way. As to the Uni, I'm sure they offer courses in English, check it out here http://www.oehweb.at/
As for costs, rent can be slightly pricy, you're looking at 300 to 500 euros for either a room in a shared house or a small studio flat. Other than that living here is quite cheap, if you are young and not to fussy about what you eat, you can live off 100 euros a week easy.
Season liftpass for the entire Tirol region is 700 euros, and that gives you access to 80 different resorts.
All in all Innsbruck is a pretty sick place, I def recommend coming here! And if you have any other questions, don't hesitate to ask.