Hello @Seongwan!
Thanks for coming. I would love to see your data analysis, even if it’s work in progress. Anything you want to share will be well received.
We call these allow and deny lists. It matters what stories make worlds, this is important for me 
To answer your questions:
Yes, any miner that misbehaves has to be removed from the allow list.
And yes, the relay can compare the bundles it sends to the miners with the blocks that land on-chain, and identify misbehavior.
There are some challenges in this relation and monitoring, which we are taking into account for the redesign.
With less than a month to go for the merge, the particulars for proof of work are less important. With mev-boost and proof of stake the role of minners is now clearly split between block proposers and block builders, and the proposer side is permissionless.
Is this useful for your work?