First of all, even when you have Push enabled, you still want to have periodic check enabled and set to 15 or 30 minutes. This will help assuring that no messages are left unnoticed in case something happens to Push in the mean time (due to the connectivity, server or whatever). That's what the developer recommends.
OK, thats interesting and logical, that makes sense.
If I do nothing with the newly arrived mails (neither on the phone nor on the PC), the display of the mobile lights approximately after 10-30 min with displaying the Aquamail notification, as if it happened, when I change the status of the inbox on PC.
If I understand you correctly, - your problem is that the led is turning on as a notification for the messages, while you don't have any new messages, right?
No, not the LED is the problem, that is ok, that it blinks so long, until I make something with the phone, the problem is the whole IPS-Display/Screen from the phone, thats lights up and show me the lock-screen with the Aquamail notification.
So, every time the program "resyncs", it notifies you that you have unread message(s). So, everything works as you've set. (And yes, Push "refreshes" its connection on a periodic basis. So, I suspect that's what triggers your notifications.)
OK, I understand this now, that's the Push refresh is here the reason, but for me, it's a glitch, that a simple resync triggers a refresh of the lock-screen notification. On a PC with Thunderbird, there was never such an extra notification. Also other mail apps with periodical mail checks makes not such repeat notifications and even my Windows Phone (with Imap-Idle) has never made such a repeated notification.
I can not see a sense in this behaviour. In my eyes, Aquamail should save the "new mail" count befor a resync and when after resync the count is the same, than don't refresh the notification.
You should use the following options in
-> Settings (Einstellungen) -> Message notifications (Mailbenachrichtigungen) ->
tap on "Notify about" (Benachrichtigen über) -> choose "New unread messages" (Neue ungelesene Nachrichten)
As i wrote, this makes my problem badly much more worse, because when I read in this suggested setting a unread mail on the PC, the phone display goes on
AND the phones notification sound rings and that for every single unread mail, that I read on the PC.
And the "sound only once" option, which can possible solve this special behaviour is also a big problem for me in other cases, when I am away from the PC, because in noisy enviroments, I hear possibly the notification for the first new mail not and until then, I become no further sound notifications from other new mails, that is a problem for me.
Please do not missunderstand me, Aquamail is really good and I hope, my broken english does not lead to think, I will only grumble or await a super-duper special feature (as I wrote, it's a normal Windows Phone behaviour), but I am wondering, that no one else seems to have this problem (Phone&PC work with email reading).
But I think, Aquamail has here either a problem (maybe in correlation with my Honor), or a missing option variant in the notification options.
But thanks again for your suggestions and patience.