Should I be working in a food kitchen with moluscum on my lower stomach/genital area?

Moluscum and work. As long as the area is covered, there should not be an issue with you working in a kitchen. Obviously, hand washing is imperative. But moluscum in the areas you mention should not preclude you from kitchen work.
Can be OK. Molluscum is an infectious virus. It spreads by direct contact. So it is most important for you to wash your hands completely before handling things in the kitchen or before contact with others.
Should be no problem. If you do have molluscum in the areas you describe then keeping them covered and good hand washing will keep this from being an issue.