My shed is pretty well ventilated and that's where I keep my bags. However, nowadays I try to keep some of each in my utility room lump and charcoal containers. If it's been damp much though, I'll leave it in the bag a while after bringing inside from the shed.
I use my leftover charcoal for grilling on the kettles, and since I started using the torch more I just leave it on the grates. I might have lump on one and briqs on the other, and I'm ready to grill on either in just a few minutes. I notice no issues if I leave the bottom vents wide open and the top closed, whether the grill is covered or not. Humidity doesn't make as big a difference when the charcoal is burning hot after torching for grilling so I'm not worried about having my grill set up with a bed of charcoal or lump ready to be lit. However, I don't leave briqs on the wsm grate overnight anymore. Only time I've had charcoal act funny was after doing that (not every time) or if the weather's really damp DURING a cook.