Nice to hear from you again.
1.) You can do an Asylfolgeantrag. In order to be successful with such a second application you need to provide convincing evidence to prove that your personal situation respectively the situation in Pakistan changed for the worse since your first application. You have to show that there is new evidence that hasn't been known or taken into account during your first process. You need to show them that you would face an unbearable situation in your home country if you were sent back.
2.) It's true that German authorities can only deport you if they have a valid proof of identity (usually the passport). Without such a document the receiving state (like Pakistan) could refuse to take you in because it hasn't been proven that you are a Pakistani citizen.
On the other hand, I found this note from the Bavarian refugee council that states that some asylum seekers who commited a crime have been sent back even if they didn't have the required documents
Source (German language): http://www.fluechtlingsrat-bayern.de/abschiebungen-nach-pakistan.html
At the moment it's not clear if they only deport delinquents or if deportation will also be extended to "normal" rejected asylum seekers.