Thanks.
Virtual Machine - Settings - General
indicates both the Name and OS as:
Mac OS X Server 10.6 64-bit
TextEdit (and all other ways to type except the windows requiring the admin username and password) work fine in the Mac OS X Server 10.6.8 virtualized in VMware Fusion in OS X 10.8.3. They work OK in all instances in OS X 10.8.3 as indicated above.
So, the problem of the reversed lowercase/capital case only shows on the windows requiring the admin username and password and only on the virtualized Mac OS X Server in Fusion. This issue is almost 100% consistent and reproducible. It happen almost always in the virtualized Mac OS X Server. But sometimes it works as expected if I try many times in a row (without changing any setting at all), switch between caps lock, reboot and try again, etc. I would say, it works wrong 9 out of 10 times or so. Really frustrating!
On the other hand, there is the problem of wrog characters indicated above: greater than (>) and less than (<) characters, which happens all the time under all circumstances in the virtualized Mac OS X Server in Fusion. Again, no problem ever in OS X 10.8.3. This issue is 100% consistent and reproducible. It happen always in the virtualized Mac OS X Server.
How to fix both problems? Thanks.