Access to a file or folder on heroku server
heroku run bash is the best way to see what is actually deployed to dynos. As for the git repo you should treat it more like a way to deploy your app (and so therefore ephemeral) than a place to store your code.
There is no way to view what is in that repo from your web browser.
If you want to get at the files in the Heroku repo you can do so by doing a git clone [repo address].
If necessary, you might be able to clone your app’s source from its Heroku Git repository using the heroku git:clone command:
$ heroku git:clone -a myappReplace myapp with the name of your app.
This command creates a copy of the Heroku-hosted repository that contains your app’s source and complete repository history. It also includes a heroku Git remote to simplify future pushes.