Aqua "ends at" marking a message as "read" on the server (IMAP) or not (POP3 doesn't have this capability).
The rest -- fetching mail with Outlook -- is between the mail service and Outlook app.
1 - For Gmail, if you also used POP3 in Aqua or "that other app" - would only return each message to a mail app (any mail app) just once. So with multiple apps, only one mail app will "see" any given message.
There is a workaround:
https://support.google.com/mail/answer/71048282 - Aqua's default for Gmail is IMAP not POP3 so the above _should not_ apply to Aqua. But could to your "other" app.
3 - For Outlook.com, I'm not aware of any such "special server side logic".
There is another downside to mixing IMAP and POP3:
Most mail services will mark as read on the server - any message retrieved over POP3.
And then that "read" status will sync over IMAP, but those same messages will remain unread in the POP3 app - since POP3 doesn't have the capability to sync read/unread with the mail server, so each mail app tracks this on its own, independently of the mail server and other mail apps.