My other concern is that when using my arm weight to hold down a chord; what is supporting the wrist? Is it the fingers? The shoulders? Am I supposed to tense up my forearm muscles to keep my wrist leveled to avoid wrist tension? All of these combined?
So I guess the main issue I am facing, is how do I properly attack a chord or octave using arm weight? My old teacher told me that I am sort of supposed to drop my arm into the chord, catch my hand and push it inwards with my forearm.
I don't think you're being unclear at all. It's certainly something I've heard about both in the real world and in print.
I do know that many others here will have more detailed and perhaps authoritative prescriptions, and I can't speak from direct, first-person experience, having been at the keyboards most of my life.
The language, though, I think gives some hints as to the root cause. After all, in some ways, the description can give a few clues as to the disposition of mind of the agent.
So, when you say "drop my arm, catch my hand, and push it inwards," that is completely alien to everything I know about playing piano.
For guitar, which is a kind of polar opposite of a keyboard instrument, it might be good advice.
About your question,
where does the prime mover come from, down to engaging at the keyboard? It depends I think greatly on the specific passage you're executing, but, leaving aside stunts like playing while standing up, or using the feet on the keyboard, it can be from the core muscles of the body, down to the hips, but I feel it mostly in the shoulders.
I think a good exercise for you would be to play the octave passages, as an experiment, using a more comfortable interval for your hands. Could be thirds, or perfect fifths (perhaps altered), and observe for yourself where the interface lies exactly for you.
All I know is, as you know, you can watch a thousand pianists, even those with a certain baseline of technique, and find a wide range of adaptations made for each.
So, you'd have to investigate by observing carefully your own approach.
I do know a lot about tendonitis, but the ones in the feet and lower legs, so I can't say anything about your specific tendons, except to offer sympathy and I do understand the challenge.
Anyway, there are people here who can and will say much more, but that's a start.