How can I protect this exterior outlet from water and prevent smoke leakage to the interior?
Let's start with the harder one here
Smoke
It looks like there's a gap in the stone to the left of the outlet. I would at least try to fill it with something (maybe caulk if you want the simplest route). Once that is done, examine the box under the cover. Make sure you don't see any other intrusion points for air. The good news is any exterior rated cover should have closed-cell foam to seal the cover itself to the outlet and box.
Water
The outlet is within 3 feet of a water source, so you're required to have a wet location cover here. The in-use cover you linked would work just fine.