Hi Daniil!
The nice thing about git and Github is that you can do all the coding on your own repository. You don't actually need any specific access for the MariaDB repository. My suggestion is to create your own fork of MariaDB (by clicking the fork button on github). Here is a very short tutorial on how to do this.
Afterwards, I propose you do your development starting with the 10.2 branch, as that is the version in-development at the moment. The other versions are in maintenance and generally only accept bug fixes. Your "official" mentor (Alexander Barkov) might have a different suggestion regarding the starting branch. Go with his suggestion if he proposes something differently.
Once your project is finished, you can submit a pull request to the MariaDB repository. That way we can perform a final review of it and then merge it.
Here's to a great summer! Good luck. :)