It's a flood and drain system... just really deep aeriation pots, that's a lot of medium per bucket.. maybe so the medium keeps roots moist in between feeding cycles and doesn't dry out?
I would assume so. With table-top flood and drain I've seen them with just a pile of hydroton to fill the top and plants just stuck in. You can wash and reuse the balls many times. Drill a bunch of 3/8" holes in the bottom of a 5 gal pail and rinse out a whole pail in the tub at once. Can put that pail inside another one to fill with bleach water first to sterilize it then rinse well and let air dry to get all the chlorine out.
Is that a carpet the buckets are sitting on? Not good. Breeding ground for molds, mildews, fungus and bugs. A tarp would be better or plastic sheet. Is there going to be problems if say all the water in that barrel ended up on the floor?
Those systems work pretty good but the way they are spaced out a lot of light goes to waste when the plants are small. Are those hoses flexible so the buckets can be grouped close then moved out as the plants get bigger?