In the coop will be much easier: you can go in the house and ignore them :)
(You might want to round the corners a little bit to prevent piling--just shoving some bedding into a pile in each corner the first few evenings might be enough to do that.)
Ah, that makes sense. And then the freaking out ones decided to come over too, for comfort or because it must be safe (because the birds there were NOT freaking out). Silly birds! :)
Nothing. Chicks get unhappy when things change.
In the new brooder, they probably wanted to go back "home" for the night. (Yes, even little baby chicks want to go home to roost at night.)
In the old brooder, has it been turned off all day? If so, it's not pre-warmed like it usually is. If it...