These pieces are nearly always veneer, so I'd probably just assume. But when you get to the last picture (the one with the 57) you can see on the top (above the 57). You can see the layer of veneer on top of the wood frame (in other words, the '57' is stamped on the wood frame; then they glued the veneer on top of that). Hope that description helps.

Is your plan to sand with an orbital sander (power sander) or by hand? You would likely be fine with 180 (especially hand sanding), but if you're nervous (and there's not much to 'sand out' like scratches), then no harm in being conservative - just might take a bit more sanding.

Stain is optional, it really depends on what look you're going for - it doesn't sound like you'll have a piece of scrap from this piece, but it's worth practicing the stain to get the hang of it.

At the risk of stating the VERY obvious, make sure you add 'remove hardware' to the first step. If you want to clean those up, you could find more info about that (boil in a vinegar solution, use barkeeper's friend, etc.).

Don't use Citri Strip!

And if you're interested, you could just google 'Tomlinson Furniture' and read about them.