1 There's an intriguing info. gap between hiving the nuc and swarming: did you inspect every seven days, what did you discover and what did you do?
2 Bees need fuel - nectar or syrup - to draw comb and I reckon they built more rapidly on the syrup than you expected, swarmed and then hit the buffers when the feed was gone and the flow over. Desertion of the surplus space is natural: no flow and fewer bees in the box.
It
is difficult for a novice to match colony development to nectar flows and space, but where I am we had a very good spring flow on which bees built strongly, a May/June drought and nectar dearth (bees sat doing nothing), a middling main flow and a nothing since. Quite a number of mine were on triple brood by May, most others on double and I lost about four swarms out of eighty colonies. What were the flows like where you are?
3 Super space will not dissuade bees from swarming, presuming you use a QX. Brood space is the vital element early on (though super space is still needed) but if the beekeeper lets the queen run out of laying space the swarm switch is flicked on and there's no way to switch it off.
Consider getting rid of the super: it's of no use now and although it's partially drawn you don't say whether there's honey or syrup in the combs. If there is, extract it and feed it back to the bees. Store the box in a mouse-proof and dry place until next spring.
You've understood that one brood box is not enough for a prolific queen (what was the type of queen supplied?) and double brood - space - will help reduce the swarming impulse next season, as will the young queen you have (what type of queen is in there now?). Suggestion: if you were to put the bottom brood box on top and feed syrup, what would be the result?
Reading a colony is acquired through instinct and observation and as the hours spent by a one-hive owner are very slight - twenty hours a season? - by about year five you'll have the hang of it. Until then mistakes will accelerate your learning, not books nor the multitude of advice that flocks to your ears; though these are meant well they may confuse, so a good option is to work out your own plan and put
that into action; if it's a total ****-up, at least you own it and will learn from the disaster.
Yes, your colony does have varroa and it's a risky strategy at your stage of the game to pretend that it's not a problem. If this sole colony dies in winter from lack of healthy winter bees you will not only lose the £240 you paid for the nuc, but back to square one: pay out again next May.
First memo: run two colonies next year, because you're unlikely to lose both in winter and can split the survivor in summer. Second memo: treat for varroa; the time for indulging all the variety of fancy alternatives lies far into your beekeeping future.