Questions about (general) language from a (professional) linguist

From the work I have been doing recently, the following questions have formed in my mind:

Is the word "hot" actually derived from "heat"? Could it be an old past tense form or something like that?

Do you speak German? If you do, how many of you would have guessed that "Schönheitsreparaturen", for the "Schönheit" bit, does not mean "defect repairs" at all, but "decorative repairs"?