Pickysaurus

Did you restart Vortex after adding them? 
You're better off adding the files in the actual UI rather than manipulation of the folders.
There's a zone to drop archives at the bottom of the mods table

Try reinstalling Origin/EA Play? 
Alternatively you can look for your old Origin manifest files and delete them. Advice on that is here: https://modding.wiki/en/vortex/developer/game-detection#originea-play

The errors are caused by your PC (or something in your network connection) preventing the extension from being downloaded from GitHub. You can download and install it manually here https://www.nexusmods.com/site/mods/875
 
Make sure you install it in the "Extensions" section of Vortex rather than in the "Mods" section.

I'm afraid so. Profiles are gone forever if they get deleted. The mods should still be in Vortex though, just not enabled on your default profile. 

No, Vortex is intended to be used on a clean game install. 

This is almost certainly caused by a broken .NET 6 install. See this post:
 

https://help.nexusmods.com/article/92-im-having-download-issues-what-can-i-do

This is a duplicate of this thread.
 
 

Please see the solution from the pinned thread here:
https://github.com/Nexus-Mods/Vortex/wiki/MODDINGWIKI-Users-Troubleshooting-NET-6-Install-Issues

I have no idea how you got into this state. Vortexposer's suggestion of two lists getting merged sounds plausible. 
There's no harm in them being there from a technical perspective. 
You might want to check the actual files which are at:
%appdata%\Vortex\fallout4\userlist.yaml %appdata%\Vortex\skyrimse\userlist.yaml If the rules exist in both files, it's safe to remove them from the UI in Fallout 4 without impacting Skyrim's list

This is a problem in your setup. See the post below for more
https://forums.nexusmods.com/topic/13483143-vortex-keeps-purging-when-i-download-and-install-a-mod/?do=getNewComment

Try this pinned solution:
 

This is covered in the pinned post: 
 

This error is caused by a third-party extension you've installed. Go to %appdata%\Vortex\plugins and delete any recently added game extensions. The last time this came up it was Battlefleet Gothic Armada 2 causing the problem. 

Vortex supports around 250-300 games, but it doesn't support every single game on the website. I suspect nobody has made an extension for the Mafia series yet. 

The game plugins are not managed by Vortex, they are managed by the game.

Something on your PC must be wiping the AppData folder - this doesn't ever happen the way Vortex works normally. 
 
Edit: The only possible way for this to have happened is if you put your mod staging folder inside your Vortex install folder. Vortex will try and prevent you from doing this. Did you install Vortex to a location outside of Progam Files? Where was your staging folder located? 

You can manually download the extension here: https://www.nexusmods.com/site/mods/196

The docs are a bit all over the place right now, but this one covers what you're trying to do https://github.com/Nexus-Mods/Vortex/wiki/MODDINGWIKI-Users-General-Moving-Vortex-to-a-new-PC

This issue is 100% caused by a bad mod setup, but you can now disable the alerts/auto-purge under "Settings -> Workarounds - > Cross-ModType Conflict Detection". This will potentially cause issues with your mods and you will likely see the "External changes" dialogue for the files that were causing this conflict in the first place. 

I'll pass this on to our team, we're tracking issues like this in the thread below
 

This is likely to be a bug but I HIGHLY recommend installing SFSE via Vortex it makes it loads easier to update/manage/uninstall 

Go to the games tab, find fallout 4 and use the little menu on the tile to manually point it to another game folder

Make sure your new drive is NTFS formatted. 
Then ensure your staging folder is on the same drive as the game in Settings -> Mods -> Mod Staging Folder. 
If you dragged and dropped your entire Steam library to a new drive that would likely cause a lot of problems. Try verifying the games in Steam to update their new paths. 

Your post has been moved to the correct forum. 
 
It's a bit awkward to find now, but there are docs for this here: https://github.com/Nexus-Mods/Vortex/wiki/MODDINGWIKI-Users-General-Moving-Vortex-to-a-new-PC