Feeding syrup during winter will cause high humidity. Use fondant or dry sugar.
Lack of insulation on the lid will cause hive humidity to condense on the bottom of the lid and rain on the hive.
There is no mold known to man that the bees can't deal with. However if the humidity is straightened out no more mold will be produced. I expect this is white mold.
Congratulations on a high over-winter survival percentage!
I'm not sure what to think about the lack of brood, but I suspect you may have missed it, likely well covered in bees.
For a quick judge of colony strength how many frames of bees are covered when you pop the lid?
Don't give the bees too much space, there is no flow yet, they should be rearing brood and expanding population near this time of year. 2 deeps might be too big for a small colony. If the bees are in a double brood box the bees will have moved up through their honey and will be mostly in the top box. Some will reverse the boxes around this time of year to force the queen down, but for back yard beekeeping I prefer to let the bees figure out how they want the brood chamber configured, they will build it out as needed.
If your small colony is down to one box, you can boost it with some brood from your large hive, or you could put it on top of a larger colony with a double screen board so the larger colony will warm the weaker colony.
Are you Akovia on BS?