Hi @Sandy :)
It depends on your legal status if you are allowed to travel or not. As an asylum seeker you are not allowed to leave the country. The same goes for people with Duldung.
If you have subsidiary protection you can travel using your home country’s passport in combination with your residence permit.
As a fully acknowledged refugee you can use the blue passport to travel to a lot of countries.
I found this website that summarises the ruling for every single legal status. But it’s in German: http://fh-blk.de/infos/auslandsreisen-fuer-fluechtlinge/
Your Ausbildung doesn’t influence the ruling outlined above. But you have the right to have a certain amount of holidays per year. Probably it’s best to talk to your boss to come to an agreement when you can go on vacation.
All the best,