Can the rodent repeller work?

Decades ago I worked for a researcher who actually studied perception in rodents. I supported the research where we actually measured the hearing of rodents. I can tell you for certain that none of the animals, which included multiple rodents, lizards, cows, south american Cavies, and even an elephant, that we tested could hear frequencies much above 20 KHz.

As to dampness, read about cathodic protection. You can mitigate metal corrosion this way but not, for example, rotting wood.