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There is a difference between your local development and your deployed project.
I assume you created your posts local. So they are saved local into your database. Local you use a filebased database defined in the settings 'django.db.backends.sqlite3' that means when you run manage.py syncdb the file is created with all tables inside. When you deploy your code to heroku the code is pushed to the server and runs from this place. This can be everywhere, so it can’t connect to your local databasefile. For your project you has to setup a database on heroku as well. I recommend to read this article. When you want to transfer your data you can create a database dump local and load all data to you heroku database. Described here and here.
Another point, you don’t run the server with heroku open or by fire python manage.py runserver. The heroku server is automatically started when your git push heroku master is done. It use the configs from your Procfile.
When you want to migrate your heroku database you has to run heroku run python manage.py migrate <app_name> than the migration is done remotely on the heroku server. You have to run this command everytime you changed a model and added a migrationfile with python manage.py makemigration <app_name>. When you did this you has to migrate you database local and remote. That means that you change the database structure to match your models. Remember the models are only a abstraction(orm) of your database.
I don’t know your project but the order sees legit. Try to imagine this as rows. first row comes first. So the last entered row is on the bottom. You can change the order of the queryset with something like.order_by('-id'). So you get all entries in reverse order.