The whole idea of a cutdown is, in the old location, to crowd them up into the supers and promote early recruitment of foragers because there is no brood so their focus will be honey. You probably can't leave all the capped brood without leaving at least a little open brood and eggs, no need to purposefully leave a frame of eggs and open brood. I would make sure I see some eggs somewhere, but they can be scattered on the mostly capped brood frames.
In the new location the idea is to have all the open brood (so their focus will be the brood rather than honey)
If you leave the old location with no queen, all the capped and emerging brood and no honey to speak of, and plenty of supers, they usually won't swarm because:
1) they have no queen
2) they have no stores
3) there is room
If the new location has the old queen, all the open brood, virtually all the honey and pollen, some empty supers (but not too many) they usually won't swarm because:
1) they have no field force
2) they have room
3) they are busy taking care of brood
In the new location the idea is to have all the open brood (so their focus will be the brood rather than honey)
If you leave the old location with no queen, all the capped and emerging brood and no honey to speak of, and plenty of supers, they usually won't swarm because:
1) they have no queen
2) they have no stores
3) there is room
If the new location has the old queen, all the open brood, virtually all the honey and pollen, some empty supers (but not too many) they usually won't swarm because:
1) they have no field force
2) they have room
3) they are busy taking care of brood