Hotmail has a server side limit for the frequency of logins (every 15 minutes, enforced after a few logins too close in time), but that's just Hotmail.
IMAP is designed for concurrent mailbox access and long-running sessions, so no issue there either.
Now, back to the issue at hand.
- First:
All my devices are configured with "no sound" (sound: "none") in global AquaMail settings, and none of them makes a sound. At all. Not on weekends, not on weekdays, days or nights.
I'm attaching a couple of screenshots.
If those are your settings already, please long press the account, select Special settings, and make sure that you don't have a per-account notifications override ("special" settings -> those that override global ones).
- Second:
I just verified that disabling notifications in global AquaMail settings does disable them.
If there is a per-account "special settings" override, on the other hand... back to previous item.
- Third:
"now can't get the default app to make sound"... judging by your mentioning its priority inbox, and its separate notifications, it sounds like Gmail app (not Email app).
That's a separate app (from mine), has its own notification settings and should not interact / interfere at all with my app, unless -- this is a Gmail account and you've set it up in AquaMail using POP3. If that's the case, please don't use POP3 with Gmail, and let the app's preset configure it using IMAP.
Finally, since you mention Spam - if you set the spam folder to "sync as spam" in AquaMail, the unread messages there won't trigger notifications.