How does having a large mempool and allowing a greater transaction ancestry set change the interaction with your peers?
How does this change your node's interaction with its peers? Do peers send data that exceeds your node's preferences and your node drops that data upon arrival or does your node inform its peers what to send?


The protocol supports a fee filtering command, simply, only relay transactions which meet a specific feerate and nothing below. This prevents pointless relaying of transactions which would result in immediate eviction from the memool. 


  If you allow more data via higher values, does your node forward previously unacceptable data to its peers once their backlog clears enough for the data to be accepted by them?


No. Wallets in Bitcoin are expected to re-send transactions periodically if they have not been confirmed. If they will successfully relay at a later date with less mempool pressure, re-broadcasting it would be required.