There's no required game length, but I would say people should be able to get the gist of the game within 15-30 minutes.

You could make a procedurally generated Foddian game, but just being procedurally generated doesn't make it Foddian. It's more about the gameplay.

I think what generally separates a roguelike from a Foddian game is that roguelikes are generally made up of different levels instead of a single large level like most Foddian games. There doesn't need to be climbing, although climbing is a really easy way to make a game feel Foddian.

As far as I know, there aren't any Foddian RPGs out there to work from, it's up to you to figure out what feels Foddian in that context.

There are no rules around what game mechanics are "allowed". You have to decide for yourself whether it fits the theme.