Older houses usually come with paneling which I think is the worst solution.

So what you need to do is get your electrical to find out what is on each panel and then you can decide from there.  

This has new: windows, carpet, trim, light fixtures, travertine tile, maple cabinets (kitchen/bath), 6 panel doors/closet doors, granite tile counters/backsplash, appliances, paint inside and out, electrical panel, concrete front step, landscaping out front, furnace. 3/1 2 car gar, big lot, starter neighborhood/home, 960 sf. ranch no basement, been on mkt for 5 days w/ an offer coming in tonight.

The monsoons are pretty intense here and the home has a lot of wood - floor, paneling, etc.

It needs floors, doors, trim, kitchen, bathrooms, removal of wood paneling, interior/exterior paint.

The painted wood paneling looks great, and I like the white mantle to tone down the dark fireplace.

Use to be most municipalities would allow you to simply replace a fuse box with a circuit breaker panel I do not know about all municipalities because codes and requirements differ according to the Authority having jurisdiction in the area but here where I live if you update the panel meaning installing a new circuit breaker system you also have to update the entire electrical system , meaning rewire the entire house. 

I am thinking about installing solar panels on my duplex.

Can that old paneling be painted over?  

Consider installing Fiberglass Reinforced Panels (FRP) without any soap dishes.