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.