(1) Is it necessary to capitalise 'what'?
I believe the following is from Aarhus University (but sadly can't link); while the example is slightly different, only a prescriptivist would argue that the reason for choosing not to use the capital does not apply equally here – there's no confusion about where the question starts if it's put in italics:
In American English, quoting from written texts is done in almost
exactly the same way as speech...
The report states that "all accidents are avoidable," and suggests
that safety officers should be "better trained."
Note that although 'all accidents are avoidable' might have been the
beginning of a sentence, no capital letter is used if this is more
natural for the flow of the text.
(2) Is a question mark necessary here?
Note the point of using a question mark. The primary purpose of a question mark is to
indicate that the sentence is a question. It's also useful for demonstrating surprise,
skepticism, uncertainty, and the unknown.
Here, the question is delimited adequately by italics if used, and identified as a question by actually being given as one. However, I see no reason not to use the question mark here: it serves the further function of signalling a pause for the reader. I wouldn't double-punctuate (?,) in this case, as it's best to avoid bloat where not essential – though I wouldn't consider a non-italic comma, or zero punctuation, incorrect in place of the italic question mark.
(3) Are (a) quotation marks, (b) italics mandatory?
Writer's Relief gives the wise advice:
.3. Some writers use quotation marks to set off thoughts, but this can
get complicated, especially when thoughts and spoken dialogue are
.2. Another useful technique is to use italics to format thoughts,
which is an effective tool when thoughts and spoken dialogue are
interspersed. This technique is becoming standard practice among
publishers—and for good reason. The different type style makes it
quite clear when a person is thinking versus speaking aloud.
Since the question is hypothetically framed here, I'd choose what I also consider the clearer option, italics rather than inverted commas.
(4) Is a comma (/colon ...) necessary before the 'quote' / exemplar?
This has been discussed before; modern practice allows a choice of the punctuation considered most suitable in any given case (among the comma, the colon, or zero punctuation).
The previous results cannot provide an answer to questions like what
is the probability of X given Y and Z because the correlations
between the variables have still not been estimated to a sufficient
degree of accuracy.
Unless the people who decided whether or not my work was acceptable had different views on English. But happily having to conform to arbitrarily applied styles is not a major consideration here.