Hi Joe,
Welcome to the Flow forum. Thank you for filling in your profile, so that we can tell that you are in Illinois, USA.
Have you joined a local bee club, got a mentor and read some books about beekeeping? I am asking because the Flow hive is not magic, it is just a different way of extracting honey. Everything else about managing the bees is exactly the same as it would be for traditional beekeepers in your area. I would guess that in your climate zone, beekeepers overwinter their hives on at least two brood boxes, not just one. If that is the case, you should do that with your Flow hive too.
Yes. Time to do a split/artificial swarm. Here are a couple of articles which give great detail on what to do when you find queen cells in your hive. In the second article, I really like the info on page 17 onwards about how to do a modified Snelgrove split, but please read both articles. They have superb information:
http://www.wbka.com/wp-content/uploads/2015/04/wbka-booklet-english-PDF.pdf
http://www.wbka.com/wp-content/uploads/2015/02/Swarm-Control-Wally-Shaw.pdf
Probably. I really think they need a second brood box before you try to get them into the super, though.
I am sure you will get more advice, but what I would do first is read the articles above. Consider a split very soon - you may have to buy or borrow extra equipment very soon. If you don’t, you may lose more than half of your colony in the next few days. Destroying the queen cells will not prevent this - you need to split and recombine later if you want to stay at one hive.
I would take off the Flow super and put on a second brood box with frames in it. Let them fill that before putting the super back on. Only put the Flow super on when all of the following rules are true:
- Every frame is mostly filled with fully drawn comb, and
- The comb is 80% full of brood, honey or pollen, and
- Every frame is well-covered with bees.
The reason is that you need enough bees to defend (from SHB, wasps and wax moths) and use the new space. When the above three items are all true, you have enough bees. 
To get the bees to use the Flow super more readily, there are a few tricks. I took 1-2cm blobs of burr comb from an inspection on my hive tool, and just pressed and smeared sideways gently onto the frame faces at about 10cm intervals. You don’t need to cover the whole frame, just put enough on to make it smell like the hive. Each frame face ended up with about 12 blobs of smushed wax pressed into it. The bees cleaned it all up within a day or two. You can also paint melted bees wax onto the frames, and there are several other tricks too, which you can search for using the magnifying glass tool at the upper right of the forum window.
