Primers & Dies OK
Yes, Yes and Definitely No.
Primers are generally best kept in the manufacturers' packaging, but leaving them in your primer feed device for a short time is OK. If they are stacked in a tube and one goes off (how that happens, I don't know, but it sometimes does) its siblings may have a chain detonation.
Dies, no problem unless your loading area has far too much humidity. I leave my dies set up in their turrets all the time. Drop a dust cover over them would be a good idea. Old pillowcase is just about ideal unless there are objections from whoever is responsible for bedclothes.
Powder, though. That may be another story. Powder has been known to etch the plastic hoppers of some powder measures. Some people believe that exposure to air (and subsequent loss of some of the volatile elements of gunpowder) will change the characteristics of your powder. Some believe that exposure to light might deteriorate the powder.
I accept these beliefs, though I have no proof of them.
If, for any reason, you forget what powder you left in the hopper, the effects can be disastrous. I recall one thread started by a guy who shared this cautionary tale. He returned the powder from his powder measure to its original manufacturer's 8-lb jug (which was half full). Then he realized that it was the wrong powder and was now contaminated with different powder. He now had 4 lbs or so of unusable powder. Good for nothing but fertilizing potted plants or entertaining the neighborhood kids with pyrotechnics.
I NEVER leave powder in a powder measure longer than a bathroom break.