The sentence is, 'マスコミにバラしてもいいんですよ？' What does this mean, literally?
Also, is this figure of speech frequently used? If it is, could you please give me some instances when it is used in daily life?
Just to make sure you don't miss this point:
The lady is trying to blackmail the principal into firing the teacher by threatening to spill the beans to the media, thereby damaging the reputation of the school.
"I'll go to the media if I have to" or something like that. As others have explained, the question mark doesn't really turn this into a question, it just indicates that the speaker is looking for a response, i.e. a hidden "Does this change your mind?" or something like that.
With all due respect, I must state that that a sentence would automatically become a question if it had a question mark at its end is a very Japanese-as-a-foreign-language-esque way of thinking. The question mark itself is a relatively new phenomenon in the history of the Japanese language; therefore, we tend to use it more freely than the speakers of other languages that have been using the question mark from the beginning.
Not sure if the members like this analogy but to me it is like sushi. Where sushi is relatively new as in North America, people make sushi more freely than the Japanese do --- like by using creamcheese and avocado or deep-frying sushi as with the volcano rolls.
The sentence 「マスコミにバラしてもいいんですよ？」 is 100% natural-sounding and "correct" by the native speakers' standards, period. Grammatically, it is a statement but is read with a rising intonation at its end, which is the purpose of the use of the question mark by the author. In informal writing, this (the combo of statement and quetion mark) is often practiced to let the reader know that speaker expects the other person's opinion or reaction to the statement. You may think of this as an un-stated "Is that OK?" or "What do ya think?"
We do exactly the same in aural conversations as well with a statement said with a rising intonation, naturally without using a quetion mark.
Finally, a couple of "real-life" examples: