Yes, sc-bee has covered this, but from a primary swarm to checking, I would not expect to find a laying queen for three weeks.
As far as an empty medium frame in a deep brood nest, if the combs on each side are deeps and full drawn with brood in them, the bees will build on the bottom bar nice and straight. But if you put two mediums together, there is no telling, they might build an angled comb spanning both frames but then they might do the same on the top bars if there is no guide and a gap equal to two frames...