To your first question: Heroku will not allow you to modify the filesystem. So your assertion is correct- You will need to pre-compile the asset pipeline before you send it up to Heroku, so that it can be utilized in your production environment.
And the latter: You'll want to make sure you have the latest compilation. Any others wont be used. The "xxxxxxx" portion is to make sure that your users have the latest and greatest version of your assets. It's a way of versioning what the browser gets, and making sure they're not caching a bad copy of the JavaScript, when you want to set up their cache to hold on to the JS and CSS files as long as they can, instead of constantly getting it from your web server.
Take my Heroku comments with a slight grain of salt, as I have not deployed to Heroku before. I just know how their system works to some degree.