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How does an Ethereum node understand that 51% confirmations have been obtained?

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In a private Ethereum setup:

  • How does a node that computed the nonce understand that 51% of the nodes have confirmed the mining?
  • Is there some kind of a counter maintained which shows number of confirmations?
  • Are the nodes which confirmed the mining rewarded with some amount of Ethers?
  • Does a node confirmation mean that along with confirming the nonce, all the transactions in the block are also confirmed?