If I have ETH in my binance account , would I automatically get the ETZ?
Honestly, in my opinion, the ethereum zero doesn't give anything to the ethereum blockchain it looks like another crap coin just like bitcoin fork coins. But it may better if binance will try to list ethereum zero in there and i sure about the binance team will be starting to distribute your token. That depends on the exchange decision.
Another coin trying to ride the popularity of Ethereum. Last year bitcoin had many forks now it's going to be Ethereum because of its popularity.