rsp After removing Caja, when I rebooted the Desktop icons disappeared.
Of course, since Caja is responsible for drawing the desktop icons in the first place.... And by the way, mixing, removing and swapping core DE components like a file manager (especially if one DE is GTK based like Mate and the other one is Qt based like Plasma) is not a particularly good idea.
rsp I have to double click to open Dolphin folders. I could not find this adjustment.
It's in Plasma settings, not in Dolphin settings. Do not try to install it on a Mate system, it's a Really Bad Idea.
Suggestions on the above shall be most welcome.
Remove Dolphin and reinstall Caja. If you really want to use Dolphin as a file manager, backup everything and install Solus Plasma from scratch (again, do not try to install Plasma alongside a GTK based DE like Mate, it's a Really Bad Idea)