Yes, they can see the address(es) which sent them bitcoin.

It depends. They can certainly see all the transactions you have made from that addresses, but not necessarily that wallet.

Most wallets are a collection of addresses. These addresses are not intrinsically linked to each other, and simply knowing one address in a wallet does not let someone deduce which other addresses belong to that wallet. If you use two or more addresses together in the same transaction, though, then that's a pretty strong indication that they are part of the same wallet.

For example. Let's say you send some coins from Address A and Address B to me in a single transaction. Most people seeing that transaction would rightly assume that Address A and Address B belonged to the same person. Next week, you send some other coins from Address A to a family member. That family member can see that Address A belongs to you, so can look back and see the other transactions which Address A has made, and be able to deduce that Address B also belongs to you. If next week you send some coins from a new address, Address C, to someone else, then your family member won't know about that address or transaction, unless you later link it back to either Address A or Address B.

The other possibility is that you make a transaction from Address D, and receive some coins back as change to Address E. If you later send those coins from Address E to your family member, then they might be able to work out that they were change from Address D, and link Address D back to you as well.

The simple answer is if you don't want anyone knowing about your other transactions, then never reuse addresses and be careful about spending change.

What do you mean by forfeited?
If that's your balance then yes, exactly it moved after it was sent. Whereas the transaction details history will never be forfeited from the blockchain, it is immutable.

^ BTC transaction was designed for having transparency and this is not all anonymity, it is pseudonymous. Once your identity is linked to that address your identity will be exposed and you can hide all your transactions not unless you will use third-party tools that can mix your coin before sending it to the destination that wants to hide, like suggested above it was a BTC mixer. All information in your wallet will be exposed too once they know what wallet address you have used. But I don't understand what is forfeited, no one can get it if that is your coin, remember always store your BTC in a wallet where you own the private key.

If it is an exchange wallet, it will be difficult to track your transaction on that wallet. Based on my experience, the deposit transaction from another wallet to our wallet in an exchange cannot be checked. This can be safe for you if you don't want your friends or your family to know your wallet balance. But if you use Metamask or MEW wallet, your transaction can be tracked.

In short, only if you stored all your bitcoin in the one address.

If you distribute them to different bitcoin addresses, then only some of your balance will be discovered (some online wallets/platforms give you only one address as explained in the replies above).

You wouldn't be so alarmed if you just didn't do any transactions to a porn site.    Yes they may see all the transactions but you can always reason. 
Seriously I also worry but it looks like they are yet not interested in such things as checking out how much BTC I have in my wallet or what transactions I do with the wallet I have.

Spreading out your BTC to a different wallet or just send altcoins to them. I do trade which is why I just send from an exchange wallet whether BTC or altcoin. If they check that wallet out, they'd really assume I'm the richest.

It didn't came to my mind the same concern as OP's concern because if we were going to talk about exchange wallet if someone or some of my relatives wanted to track down my crypto asset they would only going to see an specific amount and specific transaction I have don e but if I have disseminate my asset into different asset they woul not going to track it down. So far this I haven't take this as a primary concern because none of my relatives are being curious about tracking it down.

Indeed, I was focused on OP problem and I didn't mention this important detail. Thanks for doing so.



I did think on this "method", but I decided to not tell it because if somebody learns to look onto block explorer, it may get (rather fast) to understand such an easy move and get to follow OP funds (of course, depending on how good OP uses different addresses for different purposes - but I expect the worse in this, privacy wise).

OP has to follow above directions because that's what's best for him ,actually the wallet market is also good ,but maybe later there other questions from your family and might think that "ownership of address exchange wallet is your wallet"
may it could be that OP wants to hide his assets because "sorry" family usually borrows money or something else social jealousy in the family !

Because it is transparent, of course they will be able to see the balance and all transactions at that address. If you want to be anonymous, you can use methods such as using some mixers or sending them through an exchange.