How exactly has the wiring for the different rotors been generated? Were those generated totally at random (except that no letter can be mapped to itself), or is there some kind of algorithm to generate a "strong" wiring? Or, in other words, is any "random" wiring as secure as any other "random" wiring, or does the wiring need to have certain properties?

Specifically, is there any reason why they used a small number of rotors, each of which had a "fixed" wiring, instead of generating a unique/fresh wiring for each message (or at least for each day), e.g. by using Fisher–Yates shuffle algorithm with a PRNRG that is seeded with a value derived from a secret password and a message-specific nonce?