when I give my crypto exchange my public address of my wallet to do a transfer , does the exchange know from the address any info like the wallet I am using....or?
No the crypto exchange cannot detect which type of wallet you have your address on the only thing that they would see is the transaction history of that address which is show the total bitcoin on that address and also all the addresses that it has interacted with.
But even though it is impossible to actually get to know the type of wallet the address is on it is possible to know if it belongs to an exchange and the type of exchange it does belongs to. This is because once you send your bitcoin into the address the exchange immediately transfers it to its cold wallet address and through chain analysis it is easy to know the exchange since exchange addresses are usually publicly announced.
So for exchange it is possible but it is not possible for wallets