1. The court normally sends you a letter about registration of your main appeal (Klage) and your urgent application (Eilantrag) and inform you, on which day they were registered. For that the court must have your up-to-date address.
2. Meike is right, you can't be deported before the court has made a decision on your urgent application.
3. The court sends you its decision on the Eilantrag (Beschluss) per post. If you have a lawyer and the lawyer gave the court your letter of authorisation (mandate), the decision will be sent on his/her address, the lawyer will inform you then. Check your post.
In the first letter (about registration of the appeal) the court normally gives you 1 week time to give reasons for your urgent application (you should naturally check what is in your own letter). If you really have reasons, you (or your lawyer) must write them to the court (with proof) as soon as possible. Generally you should give reasons and proof immediately with your appeal, therefore the court won't probably wait for long.
4. If you have an "obviously unfoundet" rejection, the court should generally decide within 1 week after the time for application has been over. The court can prolong the time for decision for one week or more, if the case is difficult or if the court has too much to do. (§36.3 Asylgesetz - Asylum law). In the previous years it was often the case that the courts didn't decide for weeks or even months. Recently they've mostly decided much quicker, but it is not possible to know in an individual case. I wouldn't count with much time.