Can I “duplicate” a wallet using a backup phrase (12 words)?
Yes
Where is my balance stored?
Both wallets will scan the relevant parts of the public transaction-journal ("blockchain") to add up the amount of money controlled by the keys derived from your backup phrase - this sum is your balance.
Wallets store this sum locally, exactly where and how is likely to vary depending on the software used.
if I send from (A) to a friend's wallet (Z), would my reduced balance also show on (B)?
Yes, both wallets will learn about new confirmed transactions that affect your balance.
Wallet A might show the transaction amount as pending until it receives a confirmation, a confirmation is just a new block appearing in the public transaction journal that either contains the transaction in question or which builds on top of such a block. Wallet B learns about the confirmation in the same way and will similarly notice that the block contains a transaction that affects an amount associated with an address derived from your backup phrase. The mechanism is the same for both wallets, Wallet A has no special privileges.