Adding 50amp box directly beside electrical panel
Can't do that, regional variations are not going to allow that much of a basic violation of standard practices in any region where NEC/CEC applies at all.
You need a chunk of conduit here. If it's steel conduit, you can have 3 wires instead of 4, since the conduit is the grounding conductor in that case.
That covers 1&amp;2&amp;3.
For 4:
You can use an &quot;old work&quot; box in drywall, but I would not advise doing that with a 50A receptacle/plug given the forces involved in plugging/unplugging those monsters. Surface mounting a box on the face of drywall is unusual to say the least, and would still be a problem from the plug-force point of view. You could screw a board into the studs and mount a box on the face of that, but it would be cleaner (given that your panel is flush-mount) to just remove a chunk of drywall, drill your hole, install blocking between studs to mount a box, install your conduit and box, replace and patch the drywall, and have a flush receptacle solidly mounted.
If you were planning to drill through the stud from inside the electrical panel, that's a Very Bad Idea and I suggest you think about why that might be and then not do that.