Expanding a contraction, where the expansion is not as it would seem

Solution 1:

Considering the following data

• I didn't check my voicemail = I did not check my voicemail.
• Didn't you check your voicemail? = Did you not check your voicemail?
• *Did not you check your voicemail? (the asterisk means it's ungrammatical)

Not only is there an uncontracted sentence available for every contracted one, but there is a statement (ideally, the answer) for every question; contractions as such are just one part of question formation. Presumably the first pair of sentences above are possible answers to the second pair, right?

In fact, the second question, while grammatical, has a very stilted feel to it, like it was spoken by somebody wearing pince-nez spectacles. In a word, it's overly formal; technically, one would say it is high-register syntax in a colloquial exchange, and it gets marked as strange.
So mostly English speakers don't say things like Did you not check your voicemail?

What's going on is the mechanics of Question Formation, which consists of two steps,
in the simplest case of a yes-no question.

1. Start with a declarative sentence, e.g, He has checked his voicemail.
2. Invert the subject noun phrase and the first auxiliary verb: Has he checked his voicemail?

There are two caveant here:
(1) be is always an auxiliary verb, even if it's the only verb in the sentence
(2) if there isn't any auxiliary verb, invoke Do-Support

In the case of auxiliary verb-negative contractions, as noted, they are optional in the basic sentence.
Either hasn't or has not will work (though again, they would be used in different contexts)

• He hasn't checked his voicemail ~ He has not checked his voicemail.

If we apply Question formation to both of these, we get, respectively,

• Hasn't he checked his voicemail? ~ Has he not checked his voicemail?

That's why Did not you ..? is ungrammatical -- it's not a possible output of Question Formation.
As it says in the link, contractions are only optional in their original position.
If they're moved, they're frozen, as single words, and can't be expanded again.