I need to back up my entire DB including one table that's allocated in "Tables -> System Tables". When I try to generate the sql scripts to back up my DB this table isn't mapped in this scripts. Do I need to do something more to map this table to the scripts?
Creating scripts of objects usually isn't the best backup method.
There shouldn't be any actual tables listed under Tables > System Tables. Those should all be catalog views unless you've hacked the system objects to put one of yours tables in there.