What languages do you not speak?
What languages don't you speak?

What languages can you not speak?
What languages can't you speak?

What languages are not spoken here?
What languages aren't spoken here?

What languages is Mary not learning?
What languages isn't Mary learning?

How do I ask a "negative" question, asking what something or somebody doesn't do or is not? I feel my versions are ok (that's the way to ask), but contractions are not used (so only the first in each pair should sound natural).
Thank you Emotion: smile
KooyeenI feel my versions are ok (that's the way to ask), but contractions are not used (so only the first in each pair should sound natural).
None of your questions sound very natural because the scope of answers is too broad. Contractions are fine though for negative questions and are probably used more frecuently:

Isn't the meeting at 2 o'clock. (yes/no)
Doesn't he work as a firefighter. (yes/no)
Why didn't the train stop in ... (because... it was a fast)
Haven't you seen Star Wars. (yes/no)
Thanks Bokeh,
of course yours are ok, but they are different. I am asking what someone doesn't do, not what they do. I'm asking what something is not, not what it is...
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Contractions are fine in negative sentences.
Thanks Nona Emotion: smile
So all of my examples should be ok.
Yes, they're all grammatically possible. However, as Bokeh pointed out, I doubt you'd hear any of them in natural conversations.

Your suggestion that if people were to use that kind of construction, they'd tend to use the full version rather than the contraction was not correct - and that's what both Bokeh and Nona were saying. If we did say something like this, we'd tend to use a contraction.
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Hi Rose,
yes, they could seem strange... they are strange, actually, but if you want to know what I was thinking of...

- I am learning Japanese.
- Good. That must be an interesting language... I like Spanish. I'm learning it.
- I'm learning Spanish too.
- Really?
- Yeah. I'm also learning Chinese, Arabic, French, Italian, German, Portuguese, Russian, Jamaican creole, Swedish, Finnish...
- Wait, wait a second... that's not possible. Are you even learning Hindi?
- Yep.
- Dammit, what languages aren't you learning then?

Thank you Emotion: smile
he he! I like the sound of that show-off polyglot!

In this context, I think you could get away with saying "what languages aren't you learning"- but I think I'd tend to say "Dammit, are there any languages you aren't learning?"