- Is all you do is sit here?
- Do all you do is sit here?
Which of the two is correct? From my opinion it's the first one but it's still awkward. However, the second one also seems to make sense.
The short answer is that the first seems grammatical whereas the second is definitely not.
"All that you do is to sit here" or "All you do is sit here" are perfectly acceptable declarative sentences. Making them interrogative while retaining the infinitive does seem to lead to a doubled verb as in "Is all that you do is to sit here" or "Is all you do is sit here." The only way to make sense of the doubled verb is to assume an ellipsis such as "Is it true that all you do is to sit there."
I agree that the interrogatives so formed with the doubled verb sound awkward (or at least colloquial). That awkwardness can be avoided by using a participle instead of an infinitive.
"Is sitting here all that you do" or "Is sitting here all you do" sound better to me, but that is esthetics, not grammar.
The correct way of forming the question is
Is all you do sit here?
This follows naturally from the statement form
All you do is sit here
by the standard question-forming process of inverting the verb ("is") and the subject ("all you do").
The result sounds rather clumsy, though, so I'd recommend either rephrasing (say, as "Is sitting here all you do?"), or adding a word between "do" and "sit" - for example,
Is all you do just sit here?
Adding the extra word gives a more natural rhythm to the sentence, which is probably why some people want to insert "is", but to me at least that's ungrammatical due to repeating the main verb "is".
I would say:
Do you just sit here?
Is sitting here all you do?