Hi, Wanda. Unfortunately, most construction lumber is stored outside and this can lead to some mildew on it. But this is better than storing it inside where it tends to warp, twist, cup and otherwise move around. The best way is to store it in an open shed, but few lumber yards today do it that way since material handling is also more difficult.
As far as it affecting the strength of the wood, no it will not harm it. It should not cause you any allergy problems either, since it will be buried in the wall. If it does get wet years from now, it might grow a little easier, but the spores are everywhere and growth would occur in any case. All you need is the right combination of temperature and humidity. If it would make you feel better, you could ask the builder if you could wash it down with household bleach. But really, this would be more for your psychology than for your allergies.
As far as cracking or end checking on construction lumber, this is basically the same story. Most construction lumber has it to some degree and it will not not be more of a pathway for termites, carpenter ants or other visitors. They are quite capable of finding their way into any wood. The idea is to not give them a natural path where wood is close to dirt. Keep the wood away from the dirt and you will keep the termites away. and moisture is one of the things that draws all kinds of bugs so keep it away and you keep the bugs away.