Based on that info, I would venture that the “admin” problem is caused because your user account doesn’t have sufficient rights in a couple of the registry hives to allow Multi-Edit to create the keys it needs. We actually go to some rather extreme lengths to keep our registry footprint tiny, and it certainly is for a program of this complexity. We’d eliminate any use of the registry at all if we could, but that’s not possible, for a number of reasons. I haven’t looked at Beyond Compare’s registry footprint, but I’ll wager it doesn’t go beyond an entry in HKCU\Software, unless you specified that it register its classes, in which case there might be entries in HKCR. I believe that’s an option in Beyond Compare.
For a stand-alone install, Multi-Edit requires full rights to its own directory and subdirectories, and create rights (and the other rights usually lumped together with create) in a few registry locations. After install, it only requires create and modify permissions to a smaller subset of the registry, and some files in its <ME_PATH>\Config and <ME_PATH>\Config directories, although it’s easier to assign those rights to the directories themselves. If you locate project, session, NoteBook, program temporary, tag, or backup files in other locations, you’ll need the same rights to those locations.
As for the problem with Trita, I suspect you may not be running a Java virtual machine, either Microsoft’s (no longer supported by them), or anyone else’s. Since Trita requires one, if you aren’t running one, you’ll have to download and install one. It’s been quite a while since I last ran under NT 4, so I don’t remember of a certainty whether it had one by default, but I don’t believe it did.