ETH 2.0 with proof of stake will use 99% less electricity so will be environment friendly in comparison.
Available supply of Ethereum will also be limited from 100 000 to a maximum of 2 million per year and burning will further reduce that amount another 1-4%.
Yes, ETH will eventually be free. And it cannot be limited if it is to scale. That should be obvious.
ETH is basically a smart contract protocol which will be free (and needs to be free to scale, and will all protocols that facilitate smart contracts. But, yes, proof of stake, if they can make it to work, will be more energy efficient. Remember, ETH code is open source, so anyone can easily take this to make smart contracts of their own.
Remember also, that operating a smart contract protocol should be efficient and easy. Whereas creating and protecting a Bitcoin (its utility being a store of value) naturally needs to be difficult, hence creating and securing its inherent value, scarcity, and incorruptibility.