Django to create and change mysql database for learning purposes
If you want to learn and use MySQL, then start without anything above it - no Django, no ORM, not even a Python script. Learn to configure your mysql server (the server process I mean - doesn't have to be on a distinct computer), to work with the command-line mysql client (database creation, tables creations / modifications, adding/updating/deleting rows, and, most important, doing simple and complex queries).
While you're at it, learn about proper relational data modeling (normalisations etc) so you fully understand how to design your schemas. 
Once you're confortable with this, spend some time (should be quite fast at this point) learning to do the same things from python scripts with your python's version mysql connector.
Then if you want to learn web development and Django, well go for it. The ORM is quite easy to use when you already have a good understanding of what happens underneath, so by that time you shouldn't have much problems with this part. What you'll still have to learn are the HTTP protocol (trying to do web programming without understanding the HTTP protocol is like trying to win a car race without knowing how to drive a car - it's not technically impossible but it might end up being very painful experience), then front-end stuff (html/css/javascript) and finally the views / templates parts of Django (which should be easy once you know HTTP and html). 
You can of course jump right in into Django, but you will probably fight with way too many concepts at once and end up spending twice more time to figure out how everything works and why it works that way.
I am leaning Python programming language. I have no problems with Python. I read Python official docs, and I can write small programs in Python. I want to familiarize myself with mysql database because it is useful in learning  software development concepts. I've installed mysql database and Django on my computer. I have Ubuntu 14.04 and python 3.4 installed. I've configured Django settings to use mysql database. I tested Django connection to mysql db and all things work properly.
I am a complete newbie with web development. I didn't create my own website and I didn't start developing any web application.
My purpose currently is to master creation of mysql database and tables, making changes/migrations/queries, using Django models and Python.
Is it reasonable/possible to use Django ORM for work with mysql database without simultaneous development of a web application/local application? As I've said, I don't have my own website. I want just to try using mysql and Django together on my computer in order to get deeper knowledge as to Django and mysql in this respect. 
My final purpose is development in Python, including work with mysql database. 
Mysql without Python and Django is of no use for me.