My primers are stored all over the place, where ever there's space on a shelf, or in a drawer. Oh, and in their original containers. They DO NOTneed any special containers, or protection from anything we humans can tolerate.
The packaging is plenty of protection from whatever might harm them. Including something dropping on a box! Unless of course, you're talking about a very heavy, hard object, from a substantial height, that MIGHT pop a few.
The active propellant pellet/compound is sealed under a lacquer film that seals out humidity and MOST solvents.
If seated with the anvil tight against the bottom of the pocket, they'll fire every time. If you don't seat it right, you'll encounter a no-fire situation. IF the primer pellet is still intact after being hit but not firing, a second hit MAY fire it.
Sometimes a firing pin hit on a high primer cracks the pellet/primer compound and knocks the anvil into the primer pocket so it can't be where it should be to cause the primer compound to detonate. To work properly, the primer compound HAS to be trapped between the cup and anvil, with the anvil solidly on the bottom of the pocket. Then get hit HARD by the firing pin.