As for your second scenario, yes, that's about it. Although to be honest it's unlikely to ever go to court martial; an officer demanding impossible things happens all the time and is dealt with at the company level.
The proper term "Technical Order" is indeed salient to the Air Force, but the notional concept of a "technical order" is precisely what the parent describes and exists in all branches of service, deriving its authority from a long traceability chain that terminates as a general order issued by the Secretary of the respective branch of service, e.g. in the Navy, its functional equivalent is a "Technical Manual".
I beg to differ on distinction. Whereas both uniformed and civilian personnel are required to comply with executing technical orders per the same chain of authority, the latter is almost completely shielded from the punitive hammer of the UCMJ.
Despite seemingly popular belief, uniformed personnel maintaining military equipment simply aren't at liberty to arbitrarily fix shit that breaks however way they please using whatever support equipment/material is readily available.
Think of it this way: the general order issued would be that all uniformed personnel must comply with the explicit language of technical orders in performing routine/unscheduled/critical maintenance of military equipment---no more, no less. In turn, said technical orders specify the applicable troubleshooting, diagnostic, repair, test, documentation, etc. instructions that maintenance personnel must follow and even describe system theory of operations (albeit fairly high level; nowhere near the level of specificity adequate for an engineer).
Consider this[1] junior Air Force crew chief. He's reviewing the maintenance records (specifically, 781A records which document discrepancies, related maintenance and their associated corrective actions; maintained in parallel with mirror digital database equivalent) of an assigned aircraft because he was trained in tech school on compliance of a certain mandatory technical order[2] to do so. Everything he and all his uniformed colleagues are tasked to perform is quite literally "by the book" (of which there are many) and to be executed without deviation. In theory, nothing is left to guess work and everything is traceable, all the way down to what pieceparts of a weapon system can/can't be serviced at specific levels of maintenance. Technical order doesn't exist? Can't do it. Demonstrated proficiency at a routine task? Doesn't matter; the applicable technical order must always be present, open at task and performed to the letter at all times. In this environment, you're not authorized to wipe the ass end of an aircraft without an explicit technical order enumerating step-by-step instructions. That maintenance officer screaming at this guy's senior enlisted supervisor is in fact a logistician in company-grade uniform. Said officer can steer this airman towards court martial for a serious enough technical order deviation, but really can't do shit if exhaustive technical order compliance doesn't result in a desired outcome.
In your example, the system would be deemed "not mission capable", the required part(s) would be placed on order (whose priority shot call would be determined by the production superintendent) and you'll move on to something else until the part(s) arrive and you're directed to resume maintenance action.
[1] https://www.defense.gov/observe/photo-gallery/igphoto/200245...
[2] https://www.tinker.af.mil/Portals/106/Documents/Technical%20...