I had tried to install the additional Tagging plugin, but nothing happed. Unable to copy files in the install directory. Windows prevents this even if I sing in as administrator?
This sounds like you have the "Store" version of MusicBee, which has all kinds of issues on its own when installing 3rd-party plugins due to Windows permissions interference. Drop the MusicBee Help/About menu menu; what does the version number say, including the letter after the number?
Your "all CAPS" lyric issue is being caused by something in your system other than MusicBee, which always saves embedded lyrics in whatever case they were downloaded in. If you're not using the LyricsReloaded plugin, how DO you download lyrics before you save them, and what steps do you use to save them? If you look at the files with Mp3tag or Kid3, how do the lyrics appear?
As a possible quick fix in case the cache is stuffed with trial attempts, delete the lyrics cache. I don't know what type of MusicBee you have (Store, Installer, Portable) so I can't tell you exactly where that is, but look inside the MB "InternalCache" folder and you should see a subfolder "Lyrics"--delete everything in that folder. No it does not touch whatever is embedded in your files. If you are storing lyrics externally as text or lrc files, be sure you haven't been storing them in that folder before you empty it. If that doesn't help (or you have the Store version) you should consider doing a complete uninstall of MusicBee and install the latest 3.5.x PORTABLE version, to a folder like "C:\MusicBee," where you can easily deal with plugins without Windows permissions interference.