How to determine the remaining Bitcoin Cash after the hardfork?
1.: yes. BTC and BCH have the same transaction-history until 1st of August 2017. "...Bitcoin Cash has already been mined..." no, BitcoinCash did not exist before 1st of August 2017. BitcoinCash only "copied" the blockchain of bitcoin. (the bitcoin-cash developer had also been able to start a new blockchain theoretically for example. technically there are many possibilities.)

2.: the transactions before 1st of August 2017 have the same ids/hashes in both blockchains.

3.: yes. you can use a normal exchange-website. you can sell/buy/exchange BTC and BCH like every Altcoin too. this requires obviously that you find somebody who can and want to trade with you. you can not change BTC and BCH "directly between their blockchains" without any normal trade.