Will I get notifications that are from my paired device on ZenWatch?

Yes. When a notification shows on your phone, it will also be shown simultaneously on your ZenWatch.

 

Two ways to block notifications from certain apps on ZenWatch:  

1. Access Gear icon > Block app notifications in Android Wear app.

2. When a notificatio shows on ZenWatch, slide the screen from right to left for several times and you will see a "Block app" reminder.

 

To know more details about how to block apps, please refer to: https://www.asus.com/support/FAQ/1010149/

For other detailed information, please refer to Google website: https://support.google.com/androidwear/answer/6056843?hl=en