I'm not particularly familiar with OTRS/Znuny so I'm not sure how helpful I'll be, but happy to do my best.

First, have you double checked any logs? IIRC Znuny has a log within the webUI which would be worth checking. I'd also check Apache logs (/var/log/apache2). Perhaps Znuny also has it's own log file too (check for appropriately named file/directory in /var/log).

I'm completely guessing, but I wonder if it's some sort of permissions related error. Maybe it can't do something because it doesn't have the corect permissions to a filesystem location it wants/needs to use? Perhaps even it can't install some dependencies because it can't write to the appropriate place?

I just had a quick google and apparently there is a way to view the files related to the install in more detail. Apparently there should be a list of the files it installs and all the ones that succeed should have a green tick; any that failed should have a red cross. In your screenshot it looks like "FAQ" (under "Name" in the "Local repositories" box) might be a link? Perhaps that will give more info?

If you could share how you installed the FAQ plugin that might help? If you did it via commandline, did you do that as the Linux root user or the same user Znuny runs under (I don't recall OTTOMH but I think it might be the standard webserver user - i.e. www-data). If you ran it as root, then root may own some files/folders that the Znuny system needs write access to?