If someone lives there or has some experience in the district
Praga Północ is more than just a district; it's a huge area comprising several districts. One or two parts of ithave a poor reputation (round Pl. Hallera and the side of the zoo for example, or Brodno/Targowek which are large 1970s housing projects) but some parts are OK and most of it is safe. The bit around Kozminski is industrial but easy to get to. You probably won't be more than 30 mins away unless you end up on the other side of town.
Yes, there aren't any student halls of residence - this is an ongoing problem even fo Polish people who attend. Your best option is to contact them directly for advice - they should be able to help you.
+48 696 046 102 - is the number (mobile) for a company who advertise a private hall of residence - I don't know if it's any good or not or even where it is.
This site: dpm.uksw.edu.pl/sites/default/files/inne akademiki.odt (it's a link to an Open Office file) is from another university in north Warsaw (UKSW) and is a list of various dorms that accept people from other institutions - you'll have to deal with them directly and I suspect each gives their own students priority.