Am new in this community,the rapid increase in technology and mathematics related to Bitcoin makes me confuse,am also concerned about the safety of clients data since all transactions are done on a single public network.
There's nothing to be confused about mate. You have to know that while transactions and data on the Bitcoin Blockchain are public and accessible to anyone, users identities are not directly revealed. they are pseudonymous, which means you can't know a users identity just by looking at the transactions on the Blockchain. Although with careful analysis user data can sometimes be traced, especially with the rise of centralized bodies that require Know Your Customer (KYC) processes, removing user privacy. Satoshi didn't create Bitcoin transactions to be completely untraceable and had his reasons.
there is any development or means outside of the public Blockchain that also stores client data to ensure more privacy.
To help improve privacy, there are methods like coinjoins, mixers, and coins like Monero that prioritize user transaction privacy. Though you should be careful while using mixers as your funds might be at stake. Mixers are centralized and you are literally handing the safety of your funds to them and hope they return some clean coins.