Setting up Flask with uWSGI and Nginx is quite difficult, and even with buildout scripts it takes quite some time, and has to be recorded to instructions to be reproduced later.
If I don't plan a big load on server (it's hidden from public), does it make sense to run it without uWSGI? (Flask can listen to a port. Can Nginx just forward requests?)
Does it make sense to not use even Nginx, just running bare flask app on a port?
When you "run Flask" you are actually running Werkzeug's development WSGI server, and passing your Flask app as the WSGI callable.
The development server is not intended for use in production. It is not designed to be particularly efficient, stable, or secure. It does not support all the possible features of a HTTP server.
Replace the Werkzeug dev server with a production-ready WSGI server such as Gunicorn or uWSGI when moving to production, no matter where the app will be available.
The answer is similar for "should I use a web server". WSGI servers happen to have HTTP servers but they will not be as good as a dedicated production HTTP server (Nginx, Apache, etc.).
Flask documents how to deploy in various ways. Many hosting providers also have documentation about deploying Python or Flask.