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I understand that the miners confirm transactions from memory pool . Well...
Do the miners have their own memory pool ?
Yes, each full node has. Mempool are just all transactions stored in the nodes RAM.
How can you start a mempool ? Can anyone have a mempool that other miners can connect to ?
Yes, to have your own, run a full node, like e.g. bitcoin core.
No, there is no central mempool, but transactions are passed along from node to node. If we all would stop creating new transactions for a few minutes, most mempool would be the same.
Maybe not miners directly, but other nodes yes.
You can modify your nodes rules in regards to which transactions are accepted and which are not, yes.
You send a transaction to all nodes you are connected to at the time. Each of them checks your transactions and if its sounds according to their rules, they store in memory (mempool) and broadcast it to other nodes. This continues until almost all nodes know about your transaction. A few of these nodes are miners and eventually confirm the transaction storing it forever in a bitcoin block.