If I transfer BTC to a friend/family, they now know my wallet address, correct? Does this mean they can see all the transactions I have done from that wallet? It seems like wallet information is public except for identity, but that would be forfeited once I make a transfer, right?
If you use your own stand alone wallet, then indeed, it doesn't matter where you send funds to, the recipient will know the sender address. And all the transactions related to any address are publicly visible on any block explorer. But if you were careful, used separate addresses for various needs, didn't mix them, used different change address for all transactions and so on then the recipient will see only a tiny part of "the story".
So it depends a lot how you've used the wallet.
If you use an online wallet, it basically depends on how it's done. The custodian wallets are basically accounts on a platform and you don't really know where the funds are sent from when you make a transaction (may be or may not be that much related to you).
If you want to be on the safe side, you can indeed consider all info as visible.
Bitcoin is
not anonymous.
The usual solutions for this are:
* use of mixers (if you do please make sure it's a reputed one and you've read the FAQ page first)
* try to lose track by exchanging the coins into something else and back (but fees and possibly KYC apply)
* send Monero or such, i.e. coins designed for anonymity (which I don't really think that's what you want in this case)