What do you mean "re-tag"? When it updates the library, it will add new tracks, remove tracks that no longer exist, and load tag information for new tracks. The tracks that already were in the library, will remain unchanged.
Since I use tags i am not sure if RadioBoss will re-tag when I move an music file to a new folder. Example: I van a song in my A category but it is now moved to Recurrent Folder. Do I need to re-tag the music file to "Recurrent" or will RadioBoss do this for me? If not, I dont mind doing it just as long as Radioboss now sees the correct file in the new folder.
If you want to move the music file to a different folder and keep all settings, please do it from within the Music Library: right click, Move To Folder command. It will move the file and also update database entry with the new path.
No, whatever happens with the libraries does not affect the playlists that you have already created/saved. A music library is merely a list of files, it does not store any actual information (like tags, custom crossfade settings etc).