When setting up a server, I noticed that the environment variable process.env.PORT is used. Are there any other variables like this? Where can I see all of them?
See https://devcenter.heroku.com/articles/config-vars: there's a command that appears to tell you what your environment variables are.
$ heroku config
See if that works for you.
EDIT: it appears the heroku docs linked above are wrong. Try this:
$ heroku config -s --app