It sounds as though files on your public server host is having issues more so than ULX, but ULX is just a piece of the issue.
Both functions your having trouble with include ULX reading or writing to files on the server.
If they're both corrupted for any reason, they could cause sporadic odd issues.
Re: adding user.
While players having the trouble are connected to your server, and you at the console, run "ulx debuginfo"
It will create a file called gmod\data\ulx\debugdump.txt on the server. Attach that file here using the 'additional options' menu at lower left of the post window.
Depending on what's seen there, we may be able to proceed.
Re: adding bans/using its menu.
In our latest release version (that is, not SVN), we know of an issue that can crash servers when the ulx ban menu is opened due to corruption in the temp ban file we use. (We believe we've corrected it in SVN beta code)
Though I've never seen it crash an individual, I guess it could happen.
I recommend moving your gmod/data/ULib/bans.txt file. This will not affect any permanently banned player, only those that have been temporarily banned.
Once moved or deleted, restart the server entirely (not just a map change)
Let us know if that helped.