My question is, for those unconfirmed transactions shown in the block explorers, are they in the explorer's own mempool, or they can also be transactions from other nodes' mempool?
Would have to be the transaction from the block explorer's own mempool.
If one transaction has been on Chain.so for 24 hours but not on other explorers, does it means that this transaction is created by Chain.so, and Chain.so has not broadcast this transaction into the network?
No. Each nodes have their own set of rules to accept transactions. They can select which set of rules they want to follow or which they don't. For most nodes, they differ in the minimum relay fee. Which is the fee/kb requirement to accept transactions into the pool.
Either the transaction's fees are too low or the transaction isn't well propagated.