Dark colored steel gets hot during the day, cooks moisture out of the corn, when it cools at night the moisture collects on the steel and runs down the sides making the bottom wet. No way around it.

Can't help with the mouse issue, there has to be a hole where they can get in. "Here", my Dad had a Harvestore for HMC, my mother sold it off after he passed. When I took the base out, there was steel on top, then about 6"  of concrete and gravel in the middle. The concrete was shaped sort of like an upside-down bowl, they must have piled gravel in the middle and then filled up with crete. I don't see where mice could burrow through that, I would look around the unloader trough.