From the original sale almost all of it goes to the person who minted it, minus a small fee (around 5%) for the platform. That should be the artist, but of course there are people minting art that isn't theirs. There's efforts to catch and remove that, but a lot slips through.

From secondary market sales, the artist can get a royalty if they choose and the secondary transaction is on the same platform. Typically around 10%. The same platform requirement is an issue and hopefully a future NFT standard smart contract will build in a royalty option/.

How do you remove tokens minted by people other than the artist? Who removes it, and what stops that person or those people from removing legitimate tokens?

Either you don't, and can't, or you build a special script with a revocation list run by trusted 'Oracles' who would essentially notarize a legal claim by the artist into a blocklist of image hashes, or a whitelist of who can mint NFTs for those hashes.

Those Oracles would ideally be known parties who could be sued under the laws of their jurisdiction for lying.

If the artist is themself selling the art as an NFT, I believe so.

Yes, but there is a big problem of people other than the artist creating NFTs for other peoples art. There is nothing in the NFT process that guarantees the money is going to the "right" person.