Learn English – What does a week on Tuesday mean

Another way to phrase the sentence is, "Clarify the question by telling (saying) what you would have answered if you were asked the same question."

It is a type of conditional used for past modal verbs. Past modal verbs are could, should, would, etc. "Were" is a past tense form of the verb "to be" that applies to second-person singular (i.e. "you") and 1st and 3rd person plural ("we", "they"). In this case, "were you" is equivalent to "if you were".

We would have gone to the party, if we were invited.

is the same as

We would have gone to the party, were we invited.

in the last year means "in the last twelve months (or so) including today".

Have you been outside the country in the last year?

If you were outside the country as recently as this morning, the questioner would expect you to answer "yes", even if your trip this morning was the only time you had been outside the country.

Since in the last year impinges on the present, the present perfect is fully grammatical.

It is equivalent to "Counting backwards from today..."

last year = during the previous calendar year (e.g. 2017 -> 2016).