How to open Illustrator files in Illustrator

I think you should be able to fix your main issue by launching RegEdit.exe, then browsing to here in the tree:

  • HKEY_LOCAL_MACHINE
    • Software
      • Classes
        • aifile
          • shell
            • open
              • command

Then double-click the default value to edit it.

It is currently:

"C:\Program Files\Adobe\Adobe Illustrator 2021\Support Files\Contents\Windows\Illustrator.exe"

Change it to:

"C:\Program Files\Adobe\Adobe Illustrator 2021\Support Files\Contents\Windows\Illustrator.exe" "%1"

(i.e. Add "%1" at the end.)