A mempool is a storage space on Miner Nodes which stores the list of unverified transactions. Miners pick unverified transactions from mempool, verify them and add them to the block they are creating.

The answer is No.

Every miner node has its own Mempool.

No, it is highly unlikely.

All nodes do not receive a newly created transaction at the same time, as one node doesn’t talk to all other nodes. Here the transaction creation node transmits the transaction to its peer nodes. These peer nodes forward this transaction to their peers and so on. Thus the transaction floods all over the network.

As you see in this model, some nodes receive transactions early and some later. So, it is highly unlikely that all mempools would be in sync.

Yes, there are two possibilities.

As the storage space for mempool varies from node to node. Some nodes remove transactions with lower fees during high network congestion to add more high values transactions to the mempool.

When transactions are not verified for a long time, the transaction sender can replace this transaction with a similar transaction with Higher fees to get the transaction added to the chain quickly.