Adding on to what coinculture said, the traditional BFT nature of Tendermint consensus gives it a lot of benefits over Nakamoto consensus such as 1-block finality and safety guarantees in asynchronous environments.

Traditionally, these BFT algorithms did not work in public settings, and only worked with fixed validator sets. However, with the conceptual invention of Proof of Stake, we realized we can use cryptoeconomics to facilitate validator set changes in a public network.

And yes, 2/3 of nodes are set to be honest. However, just in case you weren't aware, it's pretty not well known, but Nakamoto consensus also has a 2/3 threshhold due to the game theoretical vulnerabilities caused by a process known as selfish mining.

Tendermint consensus is more like classic BFT consensus than Nakamoto. It provides deterministic finality/safety with every block, unlike the probabilistic 6-block safety of Nakamoto.

Yes, 2/3 are expected to be honest.

Validator membership is established in the genesis state, shared by all participants, and can be updated in arbitrary ways, as determined by the particular application running above Tendermint.