When i create a wallet at bitaddress.org i could see my balance at https://www.blockchain.com/explorer . If bitadress.org is a client sided page and shouldn't send any information to outside world and I haven’t shared the wallet address with anybody, how does the blockchain.com/explorer page know if an address is included in a wallet?
how does the blockchain.com/explorer page know if an address is included in a wallet?
Short answer: it doesn't.
Blockchain.com just looks to see if it has a record of a transaction involving the address you give it.
A transaction is something such as a bitcoin-exchange sending you Bitcoin (after you sent them dollars) or you sending Bitcoin to someone else (e.g. when buying something with Bitcoin)
Details of Bitcoin transactions are public information and are copied to every Bitcoin user (or are available to every Bitcoin user).
But you don't need to use bitaddress.org or any similar service and I wouldn't!
A little more detail.
The web-page at Bitaddress.org uses a pseudo-random number generator based on mouse movements and keyboard input to generate a random private-key.
The private-key enables you to spend Bitcoin and should never be shared with anyone else.
The public-key enables other people to send you Bitcoin, you give them the address derived from the public key.
There need be no link between bitaddress.org and any blockchain explorer. The latter just searches the blockchain for transactions involving the address you type in.
The blockchain is a ledger (or more accurately a journal) containing a record of all bitcoin transactions from the creation of Bitcoin 10 years ago. All "full-node" wallets have their own copy of the whole blockchain.
Don't trust websites
Despite the above, I would not use a public service like bitaddress.org to create my private-key. After all, we don't know if the owner of that website dishonestly keeps the private-keys (or has been hacked). Bitcoin was originally designed to be used without trusting third-party services like this. You can download a desktop-wallet and generate your private-key in the privacy of your own home on a computer that is disconnected from the Internet. That is the one of the safest ways to inexpensively create a Bitcoin wallet.
Never let anyone else generate, use, borrow or see your private-key
Never share the password to your wallet, even if you change it afterwards it is useless to do so because they can already have copied your private-key - which they can later use outside your wallet to spend any Bitcoin you later added to that wallet.
If you do not understand Bitcoin adequately you may lose all your money.
If you trust websites, you may lose all your money.
If you are not careful about these things you will lose all your money.