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.
after a server reset NodeBB doesn't start regularly anymore.
./nodebb -l --log-level verbose start
2018-08-03T07:00:55.445Z  - verbose: * using configuration stored in: /var/www/html/nodebb.freeplaying.it/nodebb/config.json
Starting NodeBB with logging output
Hit Ctrl-C to exit
The NodeBB process will continue to run in the background
Use "./nodebb stop" to stop the NodeBB server
2018-07-29T20:35:45.659Z  - info: Routes added
2018-07-29T20:35:45.663Z  - info: NodeBB Ready
2018-07-29T20:35:45.666Z  - info: Enabling 'trust proxy'
2018-07-29T20:35:45.673Z  - info: NodeBB is now listening on: 0.0.0.0:4567
2018-07-29T20:58:31.312Z  - info: [app] Shutdown (SIGTERM/SIGINT) Initialised.
2018-07-29T20:58:31.313Z  - info: [app] Web server closed to connections.
2018-07-29T20:59:38.440Z  - info: [app] Database connection closed.
2018-07-29T20:59:38.441Z  - info: [app] Shutdown complete.
[cluster] Child Process (1479) has exited (code: 0, signal: null)
Log doesn't have any traces of malfunctioning plugins or the likes. Running a
./nodebb -d start
I get this:
2018-08-03T07:02:56.411Z  - verbose: * using configuration stored in: /var/www/html/nodebb.freeplaying.it/nodebb/config.json
NodeBB v1.10.1 Copyright (C) 2013-2014 NodeBB Inc.
This program comes with ABSOLUTELY NO WARRANTY.
This is free software, and you are welcome to redistribute it under certain conditions.