Hello! Glad to hear you're resuming your sake effort.
I think that choosing to cover the rice mass with a damp covering will depend on the moisture content of the rice and your ambient humidity. I don't cover mine, but I do control the ambient humidity.
Generally, condensation on the rice, or any kind of surface water, is not very good for the koji. You want the mold to grow into the grain, not so much on the surface. That said, as long as the covering is damp, not soaking wet, it should just help the mass not dry-out, and will be fine. But it may not be needed.
Break the grain and you should see the level of growth inside it, approaching the center as the process finishes. Sweet and nutty taste and aroma should also be developing after awhile.
Assuming appropriate temperatures, I would say if you have clumping in the koji then you have enough (or maybe too much) moisture, and don't cover with dampness. If its really fuzzy, you likely have too much. If you have grains drying out and becoming hard, or you see no growth in the grain, then maybe not enough moisture.
Hope that helps, good luck.