Hi! As long as you have a Duldung, you cannot travel abroad. About the crimes, which should not have been committed: To get a Ausbildungsduldung (do you have this or a "normal" Duldung?) you have to fullfill certain requirements, e.g. you should not be convicted of bigger crimes. Details about that you can find at the page of Handbook Germany, which is in general a very reliable and good source for information:https://handbookgermany.de/en/rights-laws/asylum/ausbildungsduldung.html If you got a Ausbildungsduldung, the requirements for a residence permit afterwards are quite easy: you can also find it in the link above. What you may have read on the page of Handbook Germany are the requirements for a permanent residence permit. For this you should not be convicted of a crime