Because of the API, Your chats / notifications should be able to be done rather easily too. Just need to get the user to login via nodebb's login then you can pull notifications. How you do that is up to you and how you make it notify is also up to you.
Nodebb as the forum link. Yeah thats easy. Put nodebb in a dir of "forums" and then just link to it
Moving away from php is a good idea and seeing as nodebb and angular both use node.js it looks like you are going with the right forum software.
@h7 Thanks, this helped, in my case with no need to make the app public. It's still "In Development", but working.
The settings at Facebook for Developers are like the following:
Settings > Basic
Display Name: Example Community Login
App Domains: example.com
Contact Email: firstname.lastname@example.org
Category: Some category
Site URL: https://example.com/community/
Facebook Login > Settings
[yes] Client OAuth Login
[yes] Web OAuth Login
[no] Force Web OAuth Reauthentication
[yes] Use Strict Mode for Redirect URIs
[yes] Enforce HTTPS
[no] Embedded Browser OAuth Login
Valid OAuth Redirect URIs: https://example.com/community/auth/facebook/callback
[no] Login from Devices
Well, not sure if all this is needed, but after many tests it's working this way.
There is also the interesting video Facebook SSO for NodeBB - YouTube, which is helpful although not complete.