Is it reliable to build desktop applications using web frameworks like Django?
The idea is to
and then run a server locally so that
If that is possible and yields a reliable experience, then
I've never done this, but I can't see why not. You can use the Django REST Framework to create an API that your desktop application can talk to, in exactly the same way as you might with a JavaScript single page app.
But no, you should not use the dev server for production, even in a limited scenario like this. Apache/mod_wsgi or nginx/gunicorn are simple to set up and deploy.
For the database, it makes no difference. The Django core devs prefer postgres, but you should use whatever you are comfortable with.