Launching through Vortex simply means using Vortex to run the same program that your desktop icon does, or, since you need to use SkyUI using Vortex; to run skse_loader.exe which should be in the game's root directory. Of course you can just double click skse_loader.exe and run the game like that and not have use Vortex to launch. Make a shortcut for skse_loader.exe on your desktop and use that:)
Well the names in the screenshot appear to have Nexus filename identifiers, so try r.clicking on the mod name and choosing: 'Fix missing Ids' with luck Vortex will be able to find the correct source page if the mod is indeed from Nexus (might be a problem if the mod has subsequently been hidden?) Otherwise if the mod is from Nexus you can find the page for the mod via a search on Nexus and fill in the info by double clicking on the mod name and filling in the appropriate box. As far as I know there are no other sources of mods that use the Nexus/Vortex api for updating. I also use the source box to store the page for mods from afkmods and other sites. it doesn't notify updates, but it does make looking for them manually easier:)
