Hmm, I'm also new here and since my current character still doesn't worship Gods, I'm not very sure about how it all works. But from reading the lores, this is what I could understand:
As I understand it, an Idea can only be presented or brought to mortals by a God, but once it has, it won't go away simply because the God has died. For example, Syir, the God of Peace and Civilization, was slain by Rhysol, but it didn't mean that all cities disappeared and that the word became nothing but war. An Idea can be forgotten, but it doesn't mean it will because the God who is connected to it died.
The Idea would be more of the concept. For exemple, a human couldn't come up with the concept of what numbers are - a God had to present it to them, much like the arabic alphabet needed to be created. But once the creator died, we didn't forget said alphabet. So, an idea for an artwork will come from the PC, but the concept of what art is came from a God.
For the last question, I'd say that yes, that would make sense.
But as I said, I'm not sure this is correct, it's just my view of things. This questions actually are very interesting.
EDIT: Oh, I didn't see your last post.
Well, if you can tell me what Gossamer said about this, I'd be very interested.