When I put them in the fridge, they developed a kind of a moist surface by the next day. Should I just leave them outside in an air-tight jar? If yes, then for how long will they stay fresh?
Yes, you should store them in a air-tight jar, and the best is to store the jar in a cool place in the house. The fridge is to moist for storing cupcakes. You can store them in the jar for about 3-4 days, but they won't taste fresh any more. So I would suggest if you want to store them longer then 1 or maybe 2 days, freeze them right after they cooled down from baking. If you use a topping, you can top your cupcakes when they are thawed.