As for your first question, it all depends on what is going on in the first deep. Is it full or at least 8 frames full? Then yes by all means I would bring up a frame or 2. If you have it, replace them with drawn comb, the q will probably fill it with eggs if there are enough bees to cover it. If you do not have drawn foundation, just add foundation.
I would put the empty box on top.
If they started drawing foundation in the empty box, if you do not have drawn foundation, swap those frames into the full box.
I just added 2 drawn frames into a new hive that had five full frames. It looks like it is doing real well.