How can I update the status of the blockchain

Question

1. I issue a transaction and pass an id to the smart contract. Smart contract A retrieves data from smart contract B and uses it to check whether a condition in the smart contract is true or not. If checked, save 'id, true' otherwise 'id, false.' My first question is: should there be a transaction to save this information on the blockchain? I only have the initial transaction sending id, so how is this possible?
2. I store id, true. After some time the value true becomes false. But if the old pair was stored on the blockchain and the blockchain is immutable, how can the copy be updated?

I am using Ethereum