Modern Smokeless powder is classified as a flammable solid
Not an explosive. If your house catches fire, and it gets to your powder, you will have a short, hot very intense burn, lasting a few seconds (maybe 20-30 to burn a whole pound of powder, but probably much less). Thats all.
Common aerosol cans and household chemicals can be as bad or worse.
Black powder (the only kind of gunpowder before about 1900) is a whole different matter. It IS an explosive.
Primers are also explosives, but DOT regulations have created the packaging used for safety, and in the event of a fire, they will detonate, but the explosive force is not great, unless you have thousands, and then it is like larger fireworks. Always, always, always keep primers (and powder) in their original containers.
As to the damp, don't store them where its damp. And keep them in their original containers.
When it comes to things catching fire, that can of gas for your lawnmower and the LP bottle on your gas grill is a greater risk than smokeless powder for reloading.
And did I mention to keep them in their original containers?