Can I have my passport back while waiting for an answer on my application for protection?
No. Your passport cannot be returned as long as your application is being processed.
Anyone who has an application for individual protection in for processing has to hand in their passport. If you have applied for collective protection and are later notified by UDI that your application is going to be assessed individually, you will be asked to meet up at the police station to submit your documents.
It is not uncommon to have problems opening a bank account when you do not have a passport. There are a number of banks that will allow you to open a bank account for use in Norway as long as you have an asylum seeker card. Unfortunately, UDI does not more information about which banks will accept asylum seeker cards as ID.