You are partially correct in that stative verbs usually relate to a permanent or extended state, and you cannot use would to describe a permanent or extended state. For example, you cannot replace used to with would in these sentences:
My grandma used to live in Indonesia.
We used to live in York.
We use would about regular, habitual actions- a number of separate occasions over a period of time: that's why you can't use it for permanent of extended states.
You are also correct in saying that know can be a stative verb. If you know something, then (assuming you don't forget) it's not a temporary thing.
You can, however, use know in a non-stative way, for example if you were to say
Every time somebody asked a question, John would always know the answer.
What this means is that, on every separate occasion that a question was asked, John did, on every separate occasion, know the answer.
This link provides more background information about would and used to.