Learn English – “Frustrates the life out of me”:what does it mean

To come out is a synonym for the verb emerge, to become manifest, to become known, as with a result or a fact.

Candidate X, candidate Y, and candidate Z vied for the senate seat. Candidate X emerged the winner. Candidate Y came out at the bottom.

The class took an exam and Jane came out tops.

The class took an exam and Jane came out top.

tops = top = at the top (that is, first in a ranking)

The meaning of 'owe' in this sentence is exactly what you think it is.

The situation is normally when someone's life has been saved by another. The first person had, essentially, lost their life, and the second person had given it back to him. The first person is indebted to the second for their life - they owe it to them.

In some cultures, mostly historical, this could be a literal debt - the person whose life was saved would owe the other whatever they required, up to and including sacrificing their own life for them. Nowadays the debt is not literal, but still implies that a moral debt is owed.