If I got an NFT, and later I move my miner to another hex, will I get another NFT for that hex?

You will not receive another NFT, but you will have to rebind the existing NFT to your miner again. You can do this as long as there is no other NFT miner in that hex. If there is already an NFT miner in that hex, your NFT will become invalid and you cannot rebind it.