Although are/were are used to form questions, they don't work with met. It should be have you met [her] before? (If these two people are both present, her is not necessary; you only need it if you're talking about someone who's not there at the time).
In questions that use subject auxiliary inversion (e.g. when You are ... becomes Are you ...?), and that don't use interrogatives (e.g. who/what/where/etc.), there is an easy way to tell whether or not you're using the correct auxiliary: simply rearrange the sentence to see if it makes sense as a statement.
For example:
Are you met before? You are met before.
-versus-
Have you met before? You have met before.
The second is the only one that makes sense. That's the easiest way to figure it out.
You do have one other option here; you could use do as the auxiliary. But in this case, it can't be used with met. You'd have to switch the verb to know for that to work. And it would need to be in the present tense. The rule that I've mentioned above still applies:
Do you met her? You do met her.
-versus-
Do you know her? You do know her.
You'll know to use know because it agrees with do in tense (i.e. both simple present).
Most often, these types of questions use have, had, or do.
Questions involving forms of to be (e.g. are/were), are generally about states of being/existential, mood/feelings/emotional states, location, and actions about to occur: (e.g. Are we going to leave now?, Are you there?, Are you mad?, Were they at the party?, etc.).
Depending on the context and temporal factors, you might be able to use did. This would make the main verb present tense though. If this is after the fact, you could instead say:
Did you meet her? You did meet her.
Did you know her [back then]? You did know her [back then].
The two in the room were doing something, but the two walking in were not aware what that was.
So when they walk in they ask what it was the people (or one of them) in the room were doing.
If they would ask What did you do? or What have you done?, this would imply that they did not walk in on an ongoing action (like talking, or interrogating), but that they notice that something has happened (which has now finished, but the evidence of which is present).
Both those options would apply is one of the people in the room would appear to be dead when the two men enter.
man enters room, sees other man and an unmoving body
What did you do! Why did you kill him!?
Don't worry, he's not dead. Just unconscious.
Since the assumption in the movie is that whatever the men were doing in the room was an ongoing activity, the question is not posed as if a completed action is assumed.
Best Answer
You have understood the phrase perfectly: it is another way of saying "If you had asked..."
(My personal opinion is that it is a pointlessly pompous way of saying it; but I didn't get a vote.)
The base idiom is BE to VERB, where BE is the appropriate form of the verb be and VERB is the infinitive form of any verb. It means, approximately, "suppose", in both the senses in which that quirky word is used.
Thus, in the indicative (real) mode it means be supposed or expected to do whatever VERB names. For instance, I am to go to London tomorrow means "I am supposed to go" or "I am expected to go to London tomorrow".
In the irrealis mode, expressed with the past form, it takes the other meaning of suppose, "assume as a hypothesis". If I were to go to London (or, alternatively, Were I to go to London) means "Let us suppose that I go to London" or "If we assume that I go to London".
In your example, the author asks you to "suppose" not something which happened in the present, which would be expressed as "If you were to ask world leaders today", but something which happened in the past, a few hundred years ago. You have to 'backshift' the expression from present to past.
But you can't do that in the ordinary way, by using the ordinary past form of BE, were—because you've already used up that form in the present. The workaround in English for expressing a past irrealis is to employ the appropriate form of HAVE + the past participle of VERB: "If you were to have asked world leaders a few hundred years ago".
Notice that the same workaround is employed in the ordinary, non-pompous way of expressing the same thought: "If you asked world leaders today" is backshifted as "If you had asked world leaders a few hundred years ago".
This looks like a perfect construction, but it's not; it's the past irrealis construction.