For a 0.001 ETH transaction, about how much fee would be deducted?
The fee you pay for a ETH transaction doesn't depend on the transaction amount at all.
Currently, the current fee for a ethereum transaction is around $0.05 worth of ethereum. If you send tokens like USDT, the fee would be higher. For a USDT transaction, the current fee is around $0.1 worth of ethereum.
Note that the fees can change over time and custodial services may charge you higher fees for your withdrawals.