"Ethereum 2.0 is an upgrade to the already existing Ethereum blockchain. It aims to increase the speed, efficiency, and scalability of the Ethereum network, enabling it to address the bottlenecks and increase the number of transactions. The pseudo names for Ethereum 2.0 are Eth2 or Serenity."
This is what google tells us.And yes, the fees will be cheaper after the Ethereum 2.0 implementation. But there is still a long way to go. Ethereum 1 will be further developed, along the way the fees will also be cheaper. So it is planned.
Both Ethereum versions will exist in parallel for years.
From a technical point of view, it is a new chain and thus also a new token. This token also initially has completely different capabilities. Since the Ethereum 2.0 token on the Beacon Chain cannot be transferred back to the Ethereum 1.0 Chain, it can be assumed that a market for the ETH2 token will develop. Then the ETH 1.0 token and the ETH 2.0 token will have different rates. But since you can switch from ETH 1.0 to ETH 2.0 at any time (but not the other way around), the price for the ETH2 token should never be higher than the price of ETH. But maybe below. Translated from here:
https://www.blockchaincenter.net/ethereum-2/#wasWhat happens to the smart contracts on the previous chain?
The Ethereum 1.0 chain, including all smart contracts, will continue to exist forever. Over time, however, they will lose more and more importance because new projects use the new chain at some point.
If you want you can read this too:
https://decrypt.co/resources/what-is-ethereum-2-0