To answer the original question; yes it is ok to move brood up and down between the boxes. I do it all the time. Especially during late spring / early summer period. The critical point is to put brood over brood. Meaning if you put brood in the 2nd box, ensure brood left in the bottom box is under it.
My next point is of beekeeper equipment preference. To avoid all kinds of issues later, do not ever mix box and frame sizes for the brood chambers. Pick one size and stick with it. Standardize. Hive management is significantly simplified in flexibility and lowest cost by using the same size for everything. Being able to take a frame from anywhere and put that frame anywhere goes a long way when you are standing in the middle of a bee yard with equipment spread out, bees in the air and a thunderstorm barrelling in.
On the size equipment standardizing, my advice is whatever you do, do not let her lay in the mediums. Use the mediums strictly for honey. Medium frames just are not deep(tall) enough for the queen brood patch to reach her potential; hindering their nest growth and organization of stores. Use a queen excluder to manage the queen. Using a QE, YOU decide where the queen is and where she isn't. If you are going to use mediums for brood as well, then get rid of the deeps and go all mediums for everything. Standardize.
OK, now looking at the hive as you describe it. You have a 10 frame box of bees doing well with 7 frames of brood on the go and 1 foundation left. Conditions are that you have fair weather and at least 3 weeks of good nectar flows ahead. Given those parameters, here is what I would do.
- immediately remove the medium and set that aside for later.
- bring over a second deep box full of frames.
- set the new box down next to the hive on the upturned lid, so bees do not fall into the grass or on ground below - especially the queen. Take all of the frames out of the new box and set them aside.
- now you are going to reconfigure the hive as follows: B=brood, H=honey, E= misc drawn comb, F=foundation, P=pollen
- as much as possible use drawn comb frames. if you have only foundation that is fine, it is just alot more work for the bees. Put an empty drawn comb or a foundation wherever there is an E indicated. Wherever there is an F, put an empty drawn comb if you have.
- go into the bottom box. Get started pulling frames and transferring them into the empty top box sitting on the lid.
Top Box: 10F deep
HPBBFBBEEH
The F in the top box is that one undrawn frame from the bottom box.
(place the oldest capped and emerging brood in the top box)
Bottom Box: 10F deep
FFEBBBEFFF
(place the youngest open brood and eggs in the bottom box)
Put the newly filled top box on, put the lid on, cleanup around the hive and walk away.
What is going to happen. Bees and queens naturally work from the top down, not the bottom up. If the queen is not already on one of the brood frames you put into the top box, she will likely be up there minutes after you put the lid on the hive and walk away. She will fill out the upper box with brood. When she runs out of space to work she will move down. Nectar and honey gets pushed up. As the brood emerges in the upper box, the bees will back fill it with nectar, pushing the queen down. She will then work at filling out the bottom box. When she is done in the bottom she will try to go up again. If the top is out of space, she will bounce between the top and bottom boxes looking for work to do ... when that is occurring is she will lay in swarm cups along the bottom bars of the frames of the top box.
Give them time to work-over the new box and new frames. But not too much time as to cause the queen to be bouncing between them looking for space. Stay ahead of them and give them more space to push nectar up into, allowing them to clear some of the second box. What that means is in 1 week to 10 days after adding that second box, you will next add a queen excluder on top of the second box and THEN put that medium super on above the QE. Keep stacking your medium suppers above, as they get filled, until the flow stops. Then go harvest your medium supers of honey.
Any queen worth keeping her antenna in place is not satisfied with just one box during peak of the season. By middle of June mine are sporting 12 to 16 frames of brood on the go between the two boxes, and the hives are stacked 5 to 6 deeps tall. Some go bigger. The results are really dependent on regional conditions, how you manage the hive to those conditions, and of course the genetics.