Yeah, so then you're probably on v.1.1.2 or close to it. You need to wipe your DB, and then start over, checking out v1.0.0: cd <your NodeBB directory> && rm -rf node_modules && git checkout v1.0.0 && ./nodebb install
Depends, if you're doing largely front-end code (like embedding an iFrame to some chat application) then a widget works best. If you want to modify the API or save things into the database, then a plugin is right for you.
I think your best bet is to figure out what you need to do, and then find a plugin that does something similar, and modify that plugin, or take code from it (it's open source afterall ;))