Version 0.9 also fixes the false notification on an outgoing call:
https://github.com/ruedigergad/Skipp...l.rpm?raw=true

With respect to notifications:
Essentially, you should get everything that is also displayed as highlighted notification at the top of the screen; even information about new updates, installed software etc.

The way those notifications are shown on the watch, however, depends on the type of notification.
For some notifications, I implemented some more specialized handling such that the notifications are displayed in a nicer way.
In the worst case, a fall back mechanism is used which simply shows the name of the app causing the notification as well as the text that is shown in the notification on the device.

Edit:
Version 0.10 even adds a simple app cover:
https://github.com/ruedigergad/Skipp...l.rpm?raw=true

Edit2:
I also added a first version of an own icon.
As I didn't bother to increment the version number, this time, you might need to re-download and re-install version 0.10.