As I said earlier, there is no such thing as a "Bitcoin" that is saved. What happens is that when you receive a Bitcoin, you are actually receiving an output of a transaction. That transaction output is stored in the blockchain (it is part of a transaction included in the blockchain). The output requires a valid signature from the private key which maps to your address. Therefore what you need to keep safe is your private key, and that is what goes in the offline wallet and never touches the internet. Your offline wallet has no idea what outputs belong to you, nor does it need to know that.

When you create an offline wallet, you also create watch-only wallet. This watch-only wallet only contains the public keys and the addresses so that the watch-only wallet can be online to watch for any transactions that pertain to you. You use that online watch-only wallet to watch for transaction outputs that belong to you and when you want to spend, it builds an unsigned transaction which you must take to your offline machine to sign with the private keys. Then once it is signed, you take the signed transaction back to the online machine and broadcast it.

Yes.

Yes