x2. Window screening would work with a frame as mentioned, or I've done a hardware cloth with cardboard frame as a lid. Need to be secured down enough that a jumping chick can't knock it off (or worse yet, into the heat lamp and catch fire)
Have you taken temps in there to see what the range is between warm and cool? Is there a lid that you've made to go on top? Might want to duct tape the corners so the little gap between the lid flaps isn't open like that, as I could imagine a chick jumping up and getting caught there.
x2. Use the space you have and don't bother with buying tubs or whatnot which won't last long as a brooder. Something as simple as 3' cardboard stapled or taped to the wall of the coop to make an "enclosure" should work fine for about the first 2 weeks (after that they'll easily be able to get...