While you have a Duldung, you can study. You need to have your qualifications recognised to be admitted to university here. Many universities in Germany use this site for this process:
If you study, you will remain with a Duldung. You cannot get a residence permit due to studying. If you complete your studies, then you can get a permit (there are additional requirements for this).
If you do an Ausbildung, you can get a special type of Duldung called an ‘Ausbildungsduldng’. This allows you to stay in Germany for the duration of the Ausbildung. If you complete the Ausbildung, you can then get a residence permit.
Have you been told by a university that a passport is a requirement to study? To my knowledge, it is not but the laws on universities are different in each federal state of Germany so the rules can vary from place to place.
You can apply for permission to work if you have been at least 9 months in Germany. You have to submit a concrete job offer and description to your Ausländerbehörde. There are certain people with Duldung, for example those with ‘Duldung light’ (Duldung für Personen mit ungeklärter Identität), who are not allowed to work.