Barbara,
The option you are talking about, "After deleting a messages" is under Settings -> Look and feel (half way down the list).
That behavior is independent of the connection you have.
I am not using Exchange accounts (thankfully), - so, I don't know all the specifics.
But yes, if you expect to see about thousand messages in Aquamail, you probably should have a higher number set for "messages to cache". But I don't know how that works in Exchange - I remember there was some difference from IMAP accounts.
Just in case, - regarding for reducing the number of messages to sync, - if that number is smaller than the number of messages received within your 1-hour interval between the syncs, you may end up not loading all new messages.
I am guessing that the fact of deleting the message may trigger the synchronization with the server. (I don't know if "do not sync while the app is active" option blocks only the scheduled synchronization or all.)
In any case I don’t think the app should be trying to sync at all while it’s open.
That's your personal preference, - and some (many?) people would disagree with you. You can tolerate 1-hour delay for receiving messages. For many people that's unacceptable. And I want to know if a new message arrives while I am reading my messages or cleaning my mailbox. That's why there are configurable options.
Just in case, - that option is under Settings -> Mail, receiving -> When the app is active ("Run scheduled mail sync even when the application is open").
HTH.