Is it possible to download 1 email at 1 time every session?
I don't think that is possible (in a guaranteed way).
For the typical use of an e-mail program, you want to have
all messages to be downloaded when they are available.
But here is what you can try:
If you configure your account to connect via IMAP, and enable Push, and the server supports proper function of Push, in principle, you can receive each message the moment it arrives to the server. And then you'll be getting them one-by-one. But even in that case, there is no guarantee that you might not get two messages at once, - if those were received on the server simultaneously. Nobody would ever care to work on achieving this.
For what you are trying to achieve, you might consider alternative (likely more involved) ways, - e.g. actually parsing all incoming messages.
Kostya - the Aquamail developer - might have some additional suggestions when he is back.