Learn Russian: Этот сейф закрыт. Вы отпирали его?

This is the core of the "annulled result" rule. The first sentence tells us the safe is currently closed (закрыт). If you used the perfective отперли, it would imply the safe is still open right now. Because the state of being open was reversed (annulled), Russian requires the imperfective past.

Could отпирали mean the person tried to unlock the safe but failed?

The imperfective past can sometimes mean an attempted action, but the context here points to an annulled result. The speaker is asking if the person successfully unlocked it at some point, even though it is back in its locked state now.

Why does the first sentence use the short form закрыт instead of the long form закрытый?

Short-form participles like закрыт are used as the predicate (the core of the sentence) to describe a current state resulting from a past action. You would use the long form закрытый to modify a noun directly, like in закрытый сейф (a closed safe).

What is the difference between отпирали and the more common verb открывали?

Открывали means "opened" in a general sense, while отпирали specifically means "unlocked" with a key, combination, or latch. For a safe, отпирали is very natural, though открывали would also be perfectly understood here.