Meet fellow travellers on hospitality exchange networks: Trustroots
You can get cheap meals at the Mensa (Dining Place at the University). There are two of them in Osnabrück: One is just behind the Osnabrücker Schloss, there they normally check if you have a student ID, but they also accept Id-Cards from other universities and even foreign Ids. The other one is a little bit out of town at the Westerberg (30 minutes walking from Neumarkt), there they control the ids not very often.
There is free Internet at the University Library at Alte Münze (a few Meters from Neumarkt near Saturn). Just go inside, there are computers with internet-access.