No, I think those are only 6 x 6 panels, the squares are too big and not safe. I got mine from Bed Bath and Beyond, $20 and builds a 2x6. My squares are 9x9, closer together than that one, sorry for the bad news.
For a standard 2x4 cage, you'll need 12 grids. That box would be enough, but those grid openings aren't safe. You can get the 9x9 ones from BB&B, Walmart, and I think some other places.
I thought all grids were 14 inches guess I've just never paid attention. I usually just count the number of holes. And if there are 9 of them I get them.
NO, that is harder to find and can be quite pricey. I have mine on sheet of vinyl I got at Lowes. They had a 6 foot by 8 foot sheet for 20$ I have two cages on it though. A shower curtain works well as does a vinyl table cloth at Walmart for 5$!!
people like different things underneath. I have a layer of newspapers, a layer of towels folded in half and a single prewashed (3 times) fleece.
Some people use bedding, uhaul pads are great too. You need something absorbent under the fleece and the shower curtain or whatever as the waterproof layer next to your floor or carpet