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 thinking that a sentence automatically becomes a question if it has 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 longer.
Not sure if the members like this analogy but to me it is like sushi. Where sushi is relatively new, such as in North America, people make sushi more freely than the Japanese do --- like by using cream cheese 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 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 question mark) is often used to let the reader know that the speaker expects the other person's opinion or reaction to the statement. You may think of this as an unstated "Is that OK?" or "What do ya think?"
We do exactly the same thing in oral conversations when we say a statement with a rising intonation. Naturally, this is without using a question mark.
Finally, a couple of "real-life" examples:
A group of 4 dudes are in a house and it is about noon. Taro volunteers to cook ramen for the entire group but one of the other three says he is not hungry. Taro might say as he starts toward the kitchen:
「マジで？マサちゃんお腹空いてないんだぁ。じゃあ3人分しか作んないよ？」 For those unfamiliar with Tokyo dialect, 作んない means 作らない.
You and your friend are walking towards school when your friend says 「ヤベっ！数学の教科書家に置いてきちゃった！ごめん、取ってくる。」 Because your first class starts soon, you could not wait for him to come back. You might say: