Lightroom catalogue mess

Your last screen-clip:

Mostly Looks OK, BUT consider it is NOT a Backups folder- It is your primary working Catalog folder. Change the 'parent' folder name to "Lightroom Catalog". This will then require you to [Double-Click] on the  {Lightroom Catalog-2-v10-5.LRCAT} to open your catalog, and change in preferences to specify this new 'folder' name change, or set to the "Most Recent".

Keep your folders of  'Not Connected" stuff for a time until certain that {Lightroom Catalog-2-v10-5.LRCAT} has all your photo data that you expect. Why? Because with so many Catalog versions it is possible you have imported (and edited) some files that are in one catalog but not in another. (There are methods to correct this if needed.) 

Now when you close your catalog to shut LrC down- Change the destination to ANOTHER DRIVE for the Backups. Click on the [Choose] button in the Catalog Backup dialog window.

All the best keeping it tidy 🙂

It appears that every time LrC 'opens' it is updating and old catalog. {ie. Lightroom Catalog-2.LRCAT}

This is resulting in all the other versions {Lightroom Catalog-2-V10-2.LRCAT, Lightroom Catalog-2-V10-3.LRCAT, Lightroom Catalog-2-V10-4.LRCAT, etc}

1) First, You must open "The hightlighted catalogue is the one im using" and in Preferences/General and set the preference for this Catalog-

This setting (most recent) can cause confusion, but is the one I use-

You might be better to set it to your specific Catalog {Lightroom Catalog-2-V10-5.LRCAT} until you can sort out your system. Like this (as my catalog)-

2) Next, when you are certain that {Lightroom Catalog-2-V10-5.LRCAT} is your correct working catalog, Using File Browser, you can 'Move' all unnecessary files to a temporary backup location leaving only the current catalog and its supporting files. (The Temporary location can be later deleted when certain you have all working OK)

My ONE working Catalog, and support files, in a parent folder called 'Lightroom Catalog',  looks like this ( the {.lock} file appears when the catalog is 'open', as it is now)- Note all the similar names of the .LRCAT and the support files!

3) The {Backups} folder! It holds backups of the Catalog, saved weekly, as you are aware.

You can delete many of these, keeping only a few of the recently 'dated' folders. They are your 'lifeline' if your working catalog ever becomes corrupt and you need to restore from a backup.

IMPORTANT: When you next create a Catalog Backup- you MUST change the location to be on another physical hard-drive! Having the Backups next to the Catalog means that in the event of a Hard-drive failure you would lose EVERYTHING! Catalog & backups- the lot, gone!

Post questions again if you have any doubts about you 'tidy up'.