1.What is the mempool?
The mempool is a real time database stored on the network of nodes where unconfirmed transactions are waiting (competing) to be picked by miners so that they can be included in the next block.
2.What happens if the miners can’t keep up with the rate of the new transaction?
In that case the number of transactions waiting to be included in the next block would increase the size of mempool what results in longer transaction processing in average.
3.How does a growing mempool effect transaction fees?
Larger mempool results in increase of transaction fees because miners get to choose transactions with largest fees first and ignore the ones with lower fees until mempool shrinks. Users that want their transaction to be processed as soon as possible are also competing for priority of their transaction to be included in the next block by incentivizing the miners with higher fees.