"Rather" is an adverb, whereas "prefer" is a verb. They can never trade places because a verb cannot behave as an adverb, and vice versa. So you can say "I would rather VERB#1 than VERB#2", or you can say "I prefer NOUN#1 to NOUN#2". For example: "I would rather swim than run" or "I prefer swimming to running". Note that "swimming" and "running", being gerunds, behave as nouns. The meaning of the two sentences is the same though, just expressed differently.

It depends on the context. In general, John gives the right answer and they aren’t interchangeable. But consider I prefer that John visit me It’s my preference that John visit me. I’d prefer that John visit me. I’d rather that John visit me. (In the last two, the ‘would’ isn’t necessarily describing the result of a hypothetical- it’s used to sound softer and more polite) These have similar meanings - describing a wish. (For American speakers of English this triggers the subjunctive)

They are used interchangeably

Generally interchangeable.