Finally I found an explanation that possibly answers at least your original question. This usage of "past tense" is called 発見の「た」 (ta for discovery) or ムードの「た」 (modal ta).
Most articles about this are written in Japanese, but here's an article written in English: Another Function of the Ta-form: Discovery and Recall
In a nutshell, my understanding is that た/だ, typically after ある/いる/ない, can sometimes express the nuance of "I've noticed ...", "I've just recalled ..." or "(In spite of one's prevoius knowledge/belief,) the fact is...". It actually refers to something in the present.
Wow, you can read French! (although I have thought you can't)
- (after looking for a wallet for a while) あっ、財布、こんなところにあったのか！
Oh! There it is, my wallet!
Yeah, that is right, I have the day off tomorrow. I've just recalled that.
- (after trying to open a door) おっと、鍵がかかってた。
Oops, the door is locked.
As you can see, "fixing (or updating) one's previous knowledge/expectation" seems to be the key here. So saying 「お前、生きていたのか!」 is okay because he has believed the opponent in front of him is dead.
References (These are very long articles and I haven't read them all):