>Is this the case when the queen lays eggs in several boxes as well? Will she first fill out the entire frames in the bottom box before she moves up?
No. Sometimes she does. Sometimes she does three frames in each box for four boxes up, like a chimney.
>And when she moves up, where does she start?
Usually in the center, but sometimes the whole thing is on the south side instead.
> If she starts in the lower/center part, wouldn't she still be discouraged by such a plastic plate at the place she would like to move up?
Probably anytime there is an obstruction to her moving up and keeping the brood adjacent to the brood nest, yes she would be discouraged by it.http://website.lineone.net/~dave.cushman/excludertypes.html
Look near the bottom for "plain plywood"