You don't need a PWA to get push notification. There are providers like FCM, OneSignal etc.
What you will need is a NodeBB plugin. Kindly make a plugin request or ask quote for a custom plugin.
we can have progressive web application in Nodebb
There is already a thread on the same
Is it possible to hide posts from users? if so how?
You can control permission for user groups' view access
Is it possible to add a confirmation/approval for replies to topics? if so how?
Moderator approval ?
I see. Human bots are impossible to stop.
NoCAPTCHA is the most efficient against spam bots.
Installing NodeBB on a VPS with dependencies installed is very easy. You need to type a few commands in the terminal. The skills you would need is almost same as ability to copy paste commands from available tutorial. Try Ubuntu as OS. Good luck.