Do all minors have a global pool of transactions?
Different complete nodes have a different version of mempool. Transactions are served on the bitcoin network whenever possible. If a transaction never reaches a node, it will not include it in mempool. He would not be informed of this transaction until he was included in the block by another minor.
Miner 1 takes transaction 1 in its candidate block, so transaction 1 is no longer in the transaction pool, or does each miner have a local pool of transactions, so that every minor can take the transaction? transaction 1 in its transaction pool.
The second part is correct. Each miner creates his own candidate blocks using transactions of his own mempool. If a minor is affiliated with a managed pool, the pool operator creates a block template (including transactions) and sends the header to the respective miners attached to the pool.