If your observations tell you the fanning is for environmental reasons, then go with that. I think a lot of beekeeping skill development comes from really paying attention to your hives. And you can also experiment by making small changes and observing them in place. For instance, if you think it's too warm, or too humid, make a change that you think might ameliorate that. Stand by and watch for an hour. Did it make a discernable difference, or not?
Regarding checkerboarding the brood nest: there is a lot of confusion surrounding this and a lot of confusing terminology as well. And it makes it pretty hard for new beeks to sort out.
What I did (after long study - and very cautiously at first) was insert a single undrawn, foundationless frame on the warmest, most protected side of the brood nest, with a full frame of (highly insulating as well as nutrition-supply) honey outboard of that. (IIRC, I think I started this around the second or third week of April in a horticultural Z5/Z4 area.) I did this first on my biggest, most populous hive as a trial. The girls got it in one go and promptly drew out the frame and filled it with brood (mostly drone, at first). So I repeated this on the other side and in my other hives. This caused them to expand the brood nest laterally - and it is believed to be an anti-swarming technique. As the brood nest expanded to fully fill the box, I raised a few frames (3 or 4 in one go) to a higher box, added an empty frame on each side of this newly re-positioned bunch of brood combs, with honey or open nectar and pollen outboard of that. The girls continued to draw and fill the empty foundationless frames but now with whole, flat, frames of worker brood. As it got warmer and they raised more bees, the pace picked up and now sometimes I would slip a single undrawn frame in the middle of a group of four or five solid frames of brood. They'd draw and fill that one, too. At this point I might have a pattern that looked like this: Empty frame (mostly a placeholder for the time being)/Honey/Empty stub frame to be drawn/ Brood/Brood/Empty stub/Brood/Brood/Empty stub/ Open nectar & pollen/ capped Honey. So it might look like "checkerboarding" and even be termed checkerboarding, but it's not the same thing as checkerboarding the supers.
Checkerboarding the supers, (also an anti-swarming technique promoted by Walt Wright - read about his ideas in the Resources section on this site) which I have not really done, requires alternating filled and empty, but always full drawn frames, in the super area, not the brood nest. Being a very new beekeeper (only started in 2013) I had only a few spare drawn frames so couldn't try that this year.
The downside of opening the brood nest is that it is highly intrusive to the bees, with all the kill-the-queen or prompting of supercedure risks of messin' around deep in the hive every week or two for a couple of months. It can set them back if ill-timed. In my experience this year, however, it grows bees like mad, but that in turn raises your risk of crowding as prompt for swarming, too. It seems to have worked as intended in my second year colonies (that may be different in third year colonies). I'm not sure I would repeat it as intensively as I did this year, but we'll see.
Walt Wright's scheme is to add unfilled (but already drawn) honey storage capacity (as opposed to unfilled brood space capacity like I did this year) early on. I think both ideas are based on "tricking" the bees into believeing that they have not got the requisite numbers of bees, brood, stored food, or something else, that is vital to their assessment of whether they're good to go for swarming. Swarming is their biological intention so prevention of swarming (which is in the beekeepers' best interests, if not the bees') is to some degree to deliberately frustrate their innate biological goals. Is it good or bad for the bees to stay in one spot? Certainly bees that stay hived in one place are more likely to survive, but then they also stay living with all their comensal diseases and parasites. And bees that swarm don't make honey for beekeepers after a whole year's effort on the beekeepers' parts. (In my case I am just too fond of my queens to want to part with them.)
Walt's scheme, because it doesn't require going down into the brood area (he just plumps checkerboarded supers on top) is less labor intensive. And it works in his Mid-Atlantic area where Springs are different and longer lasting than they are in the North. If I have the wherewithall (enough drawn but empty combs) I will probably experiment with it next year as I was worn out doing the brood nest opening manipulation and constantly aware I could create a disaster.
His most useful insight (to my mind) is in noticing that the swarm "go/no go" decision is made weeks before the swarm might occur and that it could be delayed by preventing the bees from having the sense that they had done "enough" swarm preparations. And further, that delaying it past a certain point (his Reproductive Swarm Decision Point) might eliminate it from consideration for the year. Since I am barely there (the Reproductive Swarm Point) in my local season, it's too soon to know if that pans out in my area.
Now, new beekeepers might read about either of these techniques and try to apply them in the establishment year when the goal is to grow as many bees as possible and make and store as much honey for the first winter. But doing them, would be a mistake in the first year (unless you are in the Tropics where the first year doesn't end in winter's pause). At the very earliest, they might work with a strong wintered-over colony and then only cautiously. Anybody who truly "checkerboarded" (meaning alternating emptyframes/single brood combs) in the brood nest is probably asking for trouble. And in the North or Canada, that would go double. There are reasonable people who believe that any disturbance, at any point in the colony's history, to the brood nest pattern established by the bees is really bad beekeeping practice. You'll have to decide on this for yourself, in conjunction with observation of your bees, in your locale.
Chalkbrood is fungus that develops when brood is chilled. So it is an infection that needs the "right" environmental conditions to be expressed. The dormant spores are likely around in many hives, and certainly in areas which are typically chilly and damp for long periods, it's a risk, particularly if your nuc producer is saying it's a possibility. Keeping the brood nest warm will prevent it appearing, but not eradicate it, I think.
Probably more info than you needed to read. But I remember being intensely frustrated last year when trying to absorb what I needed to know to get through my first few months. Hope I haven't added to your confusion.
EDITED TO ADD THIS: For your friend who checkerboarded her nuc frames: Yes, move them back together, ASAP. There probably aren't enough bees to cover that much checkerboarded brood territory to keep it warm enough. I wouldn't wait for the next "scheduled" inspection point; it seems that urgent to me. Hopefully she hasn't lost so many bees-to-be that the colony is at risk down the road.
Enj.
. ) Anyway, I was contemplating popping the reducers out, but didn't. Today was still 30c's, in the AM, then is clouded up, rained and hailed, and dropped to like ~ 10c, so I was glad I didn't. 
