IP is generally not transferred with an NFT. There's some NFT markets that offer that as an option, but I'm not sure how it would hold up legally. It should be noted that IP is not generally transferred with any physical art purchase.

Very few current NFTs exist on-chain. A handful do, and there's the interesting case of generative art where the code that makes the art lives on-chain.

There's a push to get things on Arweave, a solution that purports to be a perpetual storage solution. In the long run, I think all art NFTs will have to go in that direction to remain credible.