I found an electrical outlet hidden behind wood paneling. Do I need to cut the paneling and remove the outlet?

No, a "buried" box whether it has an outlet in it or not is unacceptable.

This box either needs to be exposed through the paneling with an outlet or just a cover or this run needs to be replaced with one without a box.

The box must be uncovered and attached to something. The cable is Romex so I would change the box to one that has ears that would swing out when you turn the screws at the top and bottom of the box. These are usually plastic boxes. The Romex should be stapled within 8 inches of the box, but I do not think this is possible in your case. It looks like the switch box feeds a 4 in square box that is also berried. This box must have access and this needs to be corrected. You may have enough slack to feed the 4 in box directly but you still have to mount the 4 in box so you can access it

If you can be 100% certain that you can disconnect all wiring going to and leading from this box (i.e. leave it totally disconnected from all possible sources of power), you should be fine in leaving it buried behind the paneling.

When disconnecting the cables at the other ends (be sure to get both ends), you'd not only want to cap off wiring, but I'd strongly suggest labeling the cabling that you're disconnecting to indicate that it goes to a buried box and MUST NOT be reconnected.

I'd use a Sharpie™ (or similar permanent pen) to write directly on the cable housing if at all possible. Adhesive labels can fall off over time, but an attached label (maybe card-stock and a zip tie) and direct marking would be a good "belt-and-braces" solution.

It's definitely a code violation, boxes have to be accessible without cutting the wall finish - paneling in this case.

The main problem with a buried junction box is that there's no way to know that there's a splice there when troubleshooting and there's no way to inspect the work inside. Splices are common failure points and if the splice goes bad, it's a real pain to find and fix. And a bad splice can definitely heat up, so it's a fire hazard.

Think about this: even if inaccessible junction boxes were code compliant, would you trust those boxes in your wall? I personally wouldn't trust either, not the one that's dangling nor the one that's attached to the stud. None of the cables are strapped down, and I don't see any clamps where the cables enter the boxes. Who knows what kind of dumpster fire might be inside those boxes.

So I'd say just bite the bullet and fix it. If I am following the photos, you have three choices:

• Eliminate the dangling box - replace the cable that feeds these with one long enough to land right in the bottom receptacle box. (This could be a lot of work.)

• Use a NM splice repair kit. These do appear code compliant, they have a listing for repairs and don't have to be accessible. Unfortunately they are junky and make an insulation displacement splice and I just don't trust them.

• Redo that dangling box so it's accessible.

So I'd probably be going with that last option, it is not much work. You'd just remove that dangling box, set a box on the stud, and staple down the cable coming down into it.

It looks like there's enough cable to reach a box set at switch height. Even though it will just wind up with a blank cover, it will look better at switch height than at some random height. Add a short cable from that box to the receptacle below, also secured properly, splice, button everything up, and hang a picture over the blank cover.

This is simple. The box the previous person used is a standard gem box. Goto the hardware store and get yourself a pair of Madison hangers to secure the box once you replace paneling. Replace paneling with a new piece that does not have the existing outlet hole. Remove Romex from box. Put paneling up and finish it if you need to paint or whatever. Then use the gem to trace out a new rectangle hole to cut. I suggest moving the new hole to the right a few inches. Pull the existing Romex through the new rectangular hole. Slide cable into box holes with clamps. Insert box and secure with Madison hangers. Please ensure the bare copper wire is splice and attached to outlet. Trim hot and neutral wires. Done.

Cut the wires. Put this in its place. Reinstall paneling. Tyco Electronics Romex Splice Kit 2 Wire, 1/Clam https://www.homedepot.com/p/Tyco-Electronics-Romex-Splice-Kit-2-Wire-1-Clam-A22899-000/202204326

Unless you want the outlet, then just cut the paneling

Yup, simplicity itself. Put the wood panel back with a square hole just big enough for the receptacle box (not including its tabs). Diagonal it through the square hole, then settle it back into the hole so the tabs are flush with the wood (tabs on your side of the wood). Fasten down with some short 1/2" wood screws (pre-drill to avoid splitting so near the edge).

Now the box is mounted flush to the wood (well very slightly proud by the thickness of the tabs).

Now, pull the old recep out, unhook all the wires, clean the rusty gook off of them with a cloth, use a Scotchbrite pad on the bared copper parts. Clean up the box to the extent that is easy, but especially clean up the flats where the receptacle yoke will land so they are paint-free and rust-free.

Attach the safety grounds to the metal box. Attach hot+neutral to a new receptacle. Remove the little "keeper squares" from the recep mounting screws, so the yoke will have hard flush metal-metal contact with the box. That takes care of safety ground.

Fit a cover plate and you're done.

You can replace the metal box in-kind if you really want to, but I don't mind old rust if it's not continuing to get wet.