When to prepose an auxiliary in a sentence?

Question

I read this at Time.com, and it's in the second line of the third paragraph.

And wouldn’t you know it, their theory proved to be both true and statistically meaningful.

I suppose it means "And in case that you don't know, I tell you that their theory..." because I tend to understand it's structure this way:"And if you wouldn't know it, their theory..." But I only know words like 'were', 'had' and 'should' can be preposed in a subjunctive mood, and they are used to suggest an assumption.

e.g. Were I you, I would go back. = If I were you, I would go back.

And I think sentences like "Somebody wouldn't know something" suggest that He don't know nor care, but this sort of logic doesn't fit the context of the original sentence I quoted.

So here are my questions:

1. How to comprehend the quoted sentence?
2. When can/must I prepose an auxiliary?

Answer 1

"And wouldn't you know it" is a fixed phrase which means approximately the same thing as "Sure enough". It often has the connotation "It would be nice if this were not true, but we are not surprised that it is true, because the universe is not arranged for our convenience."

Like many fixed phrases in English, the grammatical structure is somewhat abnormal (it sounds archaic to me, but I cannot explain why I think that) and does not generalize. If you are still learning Standard Written English grammar, it is best not to draw any conclusions from the structure of any such phrases you encounter, and especially not to assume that other things can be said in the same way.

I must also warn you that the subjunctive is dying out of modern English. If you use it in the main clause of a sentence, like your example

?? Were I you, I would go back

this sounds archaic to the point of contrivedness. These are fine, though:

If I were you, I would go back
I would go back if I were you

and to my ear the only difference between the two is emphasis.

Answer 2

“Wouldn't you know it" isn't formally parseable; it’s a fixed phrase which announces or signposts the following statement.

I’ve never encountered this phrase used for anything except to announce an occurrence annoying or embarrassing to the speaker: “I drove twenty miles to make this presentation and wouldn’t you know it, I forgot my laptop!” Its meaning is approximately “What happened is exactly what you expect, what always happens just when it’s critical that it not happen.”

Time seems to be confusing this phrase with another signpost phrase, “Guess what!”, which is employed to announce something exciting and fortunate. But breezy imprecision has been a hallmark of the Time style ever since Henry J. Luce founded it in the 1920s—it used to be known as “speaking Lucely”.