If there are any gaps in the “outside wall” you will not have a barrier to vapor. Usually, if air can pass, so can vapor. Vapor barriers usually take care of this becuase most outside walls are not completely tight. Sprayed on insulation, like iconiene, will be a barrier. To me it makes no sense to not insulate and have a vapor barrier. It is too cheap at this stage of your project not to do it.
Hi, do you have access to the pump? You could test it by lifting the float for a second. Also there may not have been a need for it to turn on. With your house being so new, it most likely has good drainage.