1) the pigs cannot knock the grid walls down if they are all cable-tied together in a rectangle. My Badger stands up and leans his full fat weight (over 1400 grams) against the cage wall went he wants something, and there is no way that is enough to lift the opposite side of the cage up. Butting against the grids with his head won't do it either, if the grids are tied together securely. The right angles at the corners give a lot of stability. Many people use the connectors that come with the grids--these plastic, button-top things with slots for the grids under the button. Those add stability too if you push the grids securely into them. But I happen to find those very fiddly to work with. I can't connect and de-connect them quickly like I can with cable-ties (I call them zip-ties sometimes -same thing). For a long time I used them just at the tops of the corners, for added stability and perfect rectangular shape--the connectors do make the whole cage very neat and regular -- but I don't bother with them at all anymore.
2) People configure the coroplast in different ways too. Often people will construct a cage base that is like a big rectangular basin, by sharply scoring just one surface of the coroplast sheet (the lower surface) and then bending it up so there is a 3 to 5 inch high coroplast border around the whole cage bottom. (you cut the corners of course, so the coroplast can be folded upwards along the cut on all four sides, and then taped on the outsides).
Note well: For babies the coroplast sides should be much higher because they can fit through the grid holes! be sure to get the grids that have *9* squares on a side, because some of the newer grid sets have only 8 squares to a side although they are still 14 inches square. The square grid holes are therefore bigger. That is very dangerous--some full-grown pigs can get their heads stuck in those larger grid holes!!! Piggies have died that way!!
When people have these one-piece cage bottoms with sides, they either tuck the fleece up around the sides and clip it to the top of the coroplast with binder clips, or they leave the coroplast on the sides bare and just put bedding on the cage bottom. Some seem to have the grids fitted inside the coroplast, some outside. You should look at some of the pictures under Cages.
Look at DuffinVT's video again. Her coroplast appears to be on the inside (as I think most have it), meaning that the grids are outside the coroplast basin-shaped base. She has the fleece pad clipped to the sides, but at the end of the cage the pad as fallen down a little. Many pigs would take the opportunity to pull it the rest of the way down with their mouth and then sneak under the fleece and start burrowing all underneath it. Which is not good for them because it'll get damp and is not ventilated. But perhaps her piggies are not burrowers or her custom pad is to heavy for them to get under.
Duffin's type of pad is what I'd call Piggie-Momma's Delight -- custom-sized for the coroplast base it is used with, and the cotton pad and the top-layer fleece all sewn together into a single pad, easily flopped right into the cage base when changing the cage, and then instantly removable when soiled. You're on a budget, you said, and these made by piggie fanciers on this site and on Etsy, are somewhat pricey; but still cheaper in the long run than any kind of 'filler' bedding like Care-fresh or hardwood shavings. If you sew--this is definitely the way to go!! You can make your own to fit the precise dimensions of your cage. There are many instructions on this site and some are posted on YouTube.
I need things maximally flexible so I just have a coroplast border to keep my place neat (the pigs will otherwise kick hay and poops out of the cage if you have no border), and I wrap it AROUND whatever cage shape I have and tape it. I set the grids right on top of the flat base and fleece, and then place my border pieces around the grids and tape together with removable tape. If you need things really neat, it would take probably too long to make it perfect-looking like the basin-style cage bases that most people have; but when I have my configuration the same for a long time I can get it pretty neat-looking and tight around the grids even at the corners. The grids are resting on the fleece and the coroplast border is also resting on the fleece, but outside the cage, and there isn't any gap to speak of because the fleece meets the bottom of the coroplast border right outside the grid.
With the basin-type cage base (coroplast sides connected to the bottom, just folded up to make cage sides), there is no gap either.
I think your last question was about whether pigs chew on the cable-ties--I keep the connected part outside the cage, and I generally clip any excess. I have never seen my pigs biting a cable tie, but the part they have access to is very small. I occasionally cut them open and reconnect the grids in a different way, and I leave just enough slack to make a moveable hinge and to get a sharp point in to cut the tie when needed.
Now please look at all the pictures! People are very creative on this site and do all sorts of things but the basic ideas of the C&C cage are all similar and best seen rather than read.