Insulation that's moist will not be effective. There are some water pipes attached to the bottom of the joist. If you're seeing condensation, you probably need to improve your grading and roof drainage outside the foundation. Condensation will not hurt but the high moisture will make your insulation ineffective. In a new home the vapor barrier is installed between the sheet rock and the ceiling joist.
Vapor barriers help prevent moisture from getting into the insulation.
With the recent heavy rains here in CA, we had a problem of water leaking in on our split level home. There is a space between one wall and the concrete floor. The walls were not affected, and no other place had any leakage. It sounds like you have a problem with flashing between the wall and the floor. These types of leaks which are often caused by driving rains can be difficult to find.