In my experience these DO work. They contain corrosion inhibiting chemicals that help keep the terminals from building up the greenish-white powder that is commonly seen on unmaintained battery terminals.
While I have no definitive studies of my own to prove they work, my anecdotal story is that they are an easy and inexpensive way to avoid corrosion.
Yes, those parts can certainly be waxed and it will help protect the finish.
Be careful not to get the wax on the black textured pieces however. After it dries it will turn whitish and will mar the look of those parts. It's hard to remove from matte or textured surfaces.