I did this too! I found a kitten and his mother that were feral, but now they are so sweet!
I would give them a room for themselves for a couple weeks, or a dog cage, and for a little while each day, just sit in there with them, and talk to them. When they get used to you doing that, you can...
1) I agree with the apron. If you put wire on the bottom it would be harder for them to scratch around.
2) They would probably be fine, insulation would be a good idea, mainly make sure it's leak proof.
I'm sorry you lost your chicks. With the poop, that's pasting up. It hardens on their vent, and eventually they can't poop. They can die from that. If you ever see that on the other chicks, clean it off with a damp paper towel.
Good luck!
I would make sure that you buried the fencing material into the ground about 1 foot, and have the holes in the fencing small, 1/2" by 1/2" hardware cloth would be best, and you'll be fine. Also check for holes in the coop.
Good luck!