" If i full fill all the requirements to study at a university and during my studies if the court also rejects my asylum could i stay until i finish my studies. " - no you can not, If you have more than one semester left. but, If you are in your last semester, only few credits and thesis left then they will allow you to complete the degree, then they give you the chance to leave voluntarily. Even then its all depend on the ABH. Some ABH does not care at all, they just send ABH police and initiate the deportation process.
You can changes cities within the same state, it is not a difficult process, just takes 2-3 months time. But, going to a completely different state, I have no idea about that.