Just like Germans, you are supposed to own a passport or whatever equivalent that allowed you to enter the country. However, just like Germans, you are not required to carry it with you (unless you carry a weapon, which is not advisable, or are on a specific job that requires it the ID).
https://www.juraforum.de/forum/t/mit...aender.595315/
If, however, there is a suspicion you might have committed a crime (even of lesser kind), the police are allowed to hold you until you have proven your identity and right to be in the country.
Now, with respect to making copies of passports or id papers. This was strictly VERBOTEN until July 2017. Now the law has changed, but there are still strict conditions under which you can copy a passport or ID. Specifically, only the owner is allowed to copy, take a photo, or scan it; the copy needs to be permanently identifiable as a copy, for example, you have a black/white copy of an original that is in color, or you have COPY written on it.
https://www.datenschutzbeauftragter-...eises-erlaubt/