Alternative you could use the Write API, although you'd be writing a lot of the one-time logic yourself to migrate users and posts and such, and I don't know offhand of anybody using the Write API quite like that 😄
You're on track with the SSO OAuth plugin. DFP should work using the adsense plugin... if not, you can ping @baris for help.
Theming NodeBB is one of our strong points, our themes are very customisable. Almost everything can be customised including templates for each page, as well as adding additional styles, etc. Check out the quickstart theme for a shell to start off with 👍
The recommended method of sharing sessions between two separate and distinct applications is through OAuth2. We recommend this approach because NodeBB maintains its own user records, so that we can keep track of user-related metrics and other data. Relying on another database would be tricky, prone to breaking, and quite possibly dangerous.
Luckily, it's quite straightforward to get things working with OAuth2!
The first step is getting your application to expose an OAuth2 endpoint. If you're running a Node.js based app, you can use a module called OAuth2orize.