I prefer programming to clicking on links, so I would like to know if Quest uses
Inform 6, and if you can edit the pure source code.

No, Quest does not use Inform.

Similarly, Inform does not use Quest.

They are completely separate tools for creating interactive fiction.

Quest does allow you to edit the source code of your game. Sometimes it's necessary, because the GUI is quite limited in some ways and doesn't cover all of the functions.

Is it possible to view the source code of the complete game, instead of just little snippets?

Yup. 'Code View' button, up on the top bar to the right.

I can't find that. Maybe it's because I'm using the web editor on my phone, which has really bad layout.

Not on the web version; you can only see the source of one script, not the XML.
I suspect this is because of the same encoding problems that crop up if you try to edit strings containing XML in code view.

If you want to take a look at the full code, you could download the game from the "My Games" list and open it in notepad or similar. But there's no way to upload a file to continue editing, so you won't be able to change anything that way.