It's stated in the first post:
1. When I delete an email from the notification, my notifications-sound will be played again after I tap on then first "delete". How can I turn off that second playback?
When I receive an email I get a notification and the phone plays my notification sound. When I swipe the notification down to reveal the options (Reply, Delete, Mark Read) and choose "Delete" the notification sound is played again.
2. Vibration on my smartwatch does not work anymore.
I guess that doesn't need any further explanation. The notification is displayed on my Smartwatch (WearOS) but the watch does not vibrate any more (no hardware issue, vibration works on notifications from other apps).