1) What gave you the confidence?
This is correct. The tense of the sentence is correct.
Elon Musk might answer with the same tense: "Landing the rocket on land gave us the confidence to try landing on a platform in the ocean."
2) "you do not mind?" (Verb after subject)
3) "this was an unusual circumstance?" (Verb after subject)
You're right, normally the subject comes first:
"Do you not mind?"
"Was this an unusual circumstance?"
However, sometimes we invert the words for emphasis.
"YOU do not mind?"
"THIS was an unusual circumstance?"
Another very common version of the question: You don't mind?