The amount in mempool is manually adjustable?
Mempool is the pool of transaction in each bitcoin full node's memory (RAM). Depending on how much memory they have available or want to dedicate to their full node the size of it can be different. Normally they set it to a value that can contain all transactions most of the time, but it can change to bigger or smaller value. When it is smaller they usually drop low fee transactions and only keep the high paying ones that have a higher chance of being confirmed.
10 minutes later when the next block is mined, are outstanding transactions prohibited from going into the previous block if there is still room?
When the block is found it can no longer be modified otherwise it will change the third field called "Merkle Root" and make the block invalid.
How will transactions be recorded after the last block is mined in 2140?
The same way they are today assuming Bitcoin protocol doesn't change in 100 years from now.