1.You may ask: "What does it mean?"

2."What does it mean?" you may ask.

Which one is correct?

Both

In directly quoted speech, it's more common to separate the two clauses with a comma: You may ask, “What does it mean?” In the first example, the colon can replace the usual comma if you mean to give the listeners a specific list of the specific things they are allowed to say. The question mark replaces the usual comma in the second one.

Is the usage of the "s correct?

Yes

The quotation marks enclose direct speech. You can also say You may ask what it means. using indirect speech. You’ll notice that the grammar changes a little to show that it's indirect speech.

There are some differences about the way Brits and Americans usually place the quotation marks with regard to other punctuation, but both of them usually like to put question marks like yours inside the quotation marks.

What's the difference between them, if any?

The first one provides a list of questions you consider acceptable for them to ask. The second acknowledges that they themselves might have this question come to them.

What about the use of the question mark?

As above, it's fine.