Is it safe to delete the files in the Virus Chest?
See Igor's answer. If you can work with your system (boot, run applications...) so it's safe to delete that files. If you're not sure, let them there for a while. They are safe there and cannot infect your system.
Over the past 5 hours, 21 files with Trojano-180 and Dumar infections have been placed there?
If you said so... the infection was spreding into your system.
How are you right now? Did you run a full scan?
Many of them are system files, which might be important?
Some files were posted there by avast (backup purposes) other could be infected.
Like Igor said, we need to know the names (and path) of that system files.
The Avast documentation doesn't give me good advice on how to repair these files using the VRB.
See User's FAQ link on my signature and, please, browse there a little until you find VRDB explanations. Anyway, it's an automated way, you can't do (manually) so much