The Immigration Office in your university usually makes the final decision, but sometimes the German Embassy in your home country can reject your visa application outright without even forwarding it to the Immigration Office in Germany. This is the worst cast case scenario and can happen for example if you are found to possess forged documents.
No, your university in Germany doesn’t send your application documents to the local immigration office. The immigration office usually relies on documents they receive from the embassy in your home country.
The main reasons why the Immigration office might reject your visa application are:
1. They didn’t find your profile fitting for the State’s future needs.
2. There were some inconsistencies with your choice of study programme.
I have covered these reasons extensively in the article.