My electrical panel is mounted on plywood which is secured by 4 nails into a stud and the top 2x4. I want to drywall this last bit of wall. Can I pull those nails and temporarily prop the panel on something while I drywall? Do I need an electrician? Should I leave it alone and drywall around it? What should I do?
I would leave the panel as is on the plywood and install drywall right up to the edges.
Before installing the drywall carefully sneak some lengths of 1x3 or 1x4 pine boards up under the edge of the plywood with about half of its width exposed. Then screw through the face of the plywood into the pine boards in a few places to secure them in place. This will provide a decent edge to then secure the edges of the drywall to when you fit it into place butted up near the plywood edge. You might want to consider slipping some plastic end cap over the edges of the drywall before sliding the sheet in place. This would protect the edges of the drywall and provide a more finished edge to mud up against.
If the boards are installed carefully you should be able to avoid ripping away the poly moisture barrier. You may also need to do a bit of cleanup regarding that mess of coax cables.
It's probably also secured by nails behind the panel.
Actually, you don't want to do that. That plywood has an important utility purpose, it's where the power, phone and other utilities attach. You need it.
The one thing I would do is extend the plywood to span out to the joists. Feel free to lift up the cables and paint under them, might be hard to tell it's not drywall. Don't paint the cables, it's important to be able to read their markings. It's utility area, it's supposed to look ugly.