I’m sure it was one of the prophets, although I don’t recall major or minor. That doesn’t narrow it down a lot, unfortunately. (I don’t think it was one of the Psalms; God doesn’t usually speak directly in the Psalms anyway, so only a few of those might even possibly count.)
Yes, there are several other times that God swears by Himself because He has no other higher to swear by (as Paul and/or the Hebraist put it). I don’t exactly recall that the place I’m thinking of has God swearing upon Himself, but I wouldn’t be surprised if it did. You’re right about Him in effect pledging His own life to fulfilling what He promises, Johnny, at the Akedah and elsewhere, but I’m sure it was more explicit: I was very surprised to read it because I wasn’t actually ever expecting to see that part of my theology just stated outright in the scriptures like that. 
(In the specific version of trinitarian theism metaphysics I advocate, the eternal ongoing self-existence of God depends on the faithfulness of the Persons to fulfill fair-togetherness toward and with one another. If they ever acted toward fulfilling non-fair-togetherness between persons, God and all the rest of reality would cease to exist. I’m not sure that the English translation “righteousness” was used in the verses I’m thinking of, but it might have been…)
God was speaking to Israel, I think, but I’m not entirely sure about that; might have been to someone more specifically. 
Thanks for both of your helps, so far, btw. 