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?
yes, the bitcoin recipient can check your transactions and they can also see the balance in your wallet.
If you don't want other people to see your balance then use another wallet as a backup wallet so that the balance in your main wallet is not seen by other people or your family.