Is there any way to not allow reading and writing contract from ethereum blockchain explorer?
One can view contract code, ABI, and every other information once the owner verifies contracts. Is this correct or not?
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If you want to restrict access to the contract you can for example require that the sender is in a list of allowed addresses. Otherwise, in general, contracts are open for everyone. Etherscan just provides an easy-to-use interface to find them and to interact with them.
So even if Etherscan has the possibility to write to the contract it doesn't mean that the writing would be successful. If you have access restrictions the writing transaction will simply fail for those who are not allowed to write.
But in general you can't stop people from reading your contract. Etherscan just makes the reading easier, but contracts can be read without the source code and without Etherscan as well. In general there can't be any secret data in Ethereum blockchain.