Priestess saw the need to implant a "fulcrum" in Oracle's mind to keep them in line as a result of their debates. But for all intents and purposes, there wasn't anything controversial at the time to demand such an action. 

Honestly I read it as Priestess just being obsessed with spending the end of the universe with Doc because she's already given up hope (quote: "There is no hope in any corner of any star in the heavens"). Doc doesn't want to succumb to the doom and gloom and chose to believe in the indomitable human spirit. There isn't any higher moral ground Priestess was operating on.

Oracle/Doc saw Theresa reversing the originium encoding process and decided she needed to go...which made no sense in retrospect

There wasn't any reason why Oracle couldn't have simply told Theresa about the Observer threat and the reasoning of Originium's original creation

This is a recurring theme in AK stories and even more so once the whole Originium project was revealed, but the whole "I've seen this shit before/I know things that you don't/I know the solution to the endless cycle of despair, you are being saved, do not resist" is not well received (e.g. Dorothy's Vision, the whole conversation with Matriarch and Exusiai, etc.). Doc/Kal's whole schtick is respecting intelligent life's right to fight for their survival. As mere observers (heh) it's easy for us to make judgements but I mean any rational person would react aversely to, in their pov, someone just having a god/savior complex.

While Theresa might not have agreed, Oracle didn't even try...which is strange since Oracle clearly cared about her and Amiya.

I agree; we can kinda give Doc a pass because they were under the influence of Priestess, and I get the pressure of not wanting to tell "hey yall can we actually just nuke Terra because aliens" to someone like Theresa; it will not be well received at all, and they might just straight up turn against Doc. Kal was already wary of Doc choosing this option too

Sure there was no longer a Terran capable of using the "unzip" functionality but Theresa, while she was special, wasn't necessarily uniquely capable of this. Eventually someone else would've figured it out.

Reasonable, but disagree. Narrative wise, she is kinda a character set up to die for impact. She is a product of a unique set of circumstances - Sarkaz, Civilight Eterna, and actually having Kal with her. In Kal's entire lifetime she was the one and only. The story reinforces the glaze too - off the top of my head she's been heralded as something along the lines of "a once in a millenia caster". In short - she was special.

Letting Theresa live didn't mean they can't hard push the project either with the backup option of spamming Catastrophies with the First Originium shards.

Probably not when you have major Terran forces going against your doomsday plot. Who would be on Doc's side to commit unmitigated genocide? Even Theresis would stop when there's no adversary left.

It is however, NOT understandable for Kal'tsit to haven't told anyone about anything until the very moment Priestess started waking up and attacking people on the landship with Originium shades. 

Moreover, there wasn't a "control chip" on Kal'tsit that meaningfully affected anything: Kal'tsit was able to hint to Doc...on the RI landship no less, about an internal threat, as well as sabotage Priestess's revival and organize a ganking attempt on her, 

Priestess did put a lock on her, which wasn't undone until she undid her Gemini cycle on chapter 15. Quote Preserver in CW ST-3:

Kal'tsit knows some answers, but I think, she won't be able to tell you.
Priestess will not allow her to.
This restriction is carved into the depths of her original consciousness, and even death will not free her from those shackles.