Warning- any preemergent (Preen) will prevent new flowers from putting out new roots and getting established. I am a big fan of pre-m and use it regularly, just wait a few weeks after planting before applying this product.Then spread something like Preen in the flower bed.
I presume this is on the basement interior, coming through from the outside. It would be very unusual for mulch to cause this problem. Mulch helps keep soil moisture even and from drying out too fast. If you have this much moisture, then I suspect it is due to poor drainage- either heavy soil, poor grading, etc.The basement wall right at this site has effloresence that I think is likely from moisutre instrusion through the foundation brick wall.
Putting topsoil on top of weed fabric will completely waste your money. And I understand that you want to plant this area, so you will need to cover the weed fabric with 4-6 inches of topsoil.:no: Weed fabric goes on top of the soil and is covered by mulch.
Frankly, according to your question it sounds like you need to either plant or put down a moisture barrier. You could remove some of the soil to a proper grade, cover with heavy plastic, and then cover the plastic with mulch. But you won't get anything to grow if you do this. Well, maybe I shouldn't say anything.