1. Starting with my only left the jeep stranded example, semi float rear axle shaft bearing = replace shaft carry a spare (finding a 35 spline spare might be tough though)
This is the single BIGGEST reason why I NEVER recommend semi-float shafts when doing an axle upgrade. Even on a 60, the shaft can break and it's happened to me. Full float is the only way to go. This is also why for factory axles, I typically recommend AGAINST custom shafts with higher splines. It's always easier to find or bum a spare off of people who all have the same thing.
2. front axle shaft break or U joint break / drive shaft U joint break = either remove axle or drive shaft and run without or trail replace a U joint so carry some spares. Can you run the front axle with 1 shaft shaft pulled or will it puke the oil down the tube? Any reason to carry a spare front unit bearing? not sure i have heard of many breaks. Dont think i have all the tools necessary to trail swap a U joint though... yet
On a JK or newer, you can pull the shaft and keep going but you will want to plug the tube with something. A sock or a rag will work but better the seal the better. Of course, running chromoly shafts with full circle clips alone will do wonders to prevent a break in the first place. 99% of the breaks I've seen have come from bearing caps that have come free due to c-clips working themselves off and that leaves the trunion to just tear through everything. Your unit bearing should let you know it's going bad before it's a real problem so no need to carry a spare in my opinion. Or, so long as you're paying attention to your Jeep.
3. Steering, I've trail fixed a bent tie rod. is it worth carrying a spare TRE? i have all the tools to swap that if i need. Sector shaft (good luck), any benefit to having a spare sector shaft or just a whole steering box? either way trail repair sounds miserable.
If you're running a tie-rod with ends that can be replaced, sure, carrying a spare isn't a bad idea but it isn't too common to see them break. The ones I have seen go were aftermarket ones like on a Steer Smart and on tie-rod flips. A sector shaft is great to have and I carry one on Moby - mainly because I've broken one on the trail. It is a big pain to replace on the trail and a spare box would make life easier but if you have ram assist, you can actually get by... just get by without one. Also, there are ways to steer without a steering box. Just a pain.
4. Ring and pinion. should you break some teeth is it best just to remove the ring gear / locker / axle shafts, leave the drive shaft and pinion attached? what do you remove in that case to get you off the trail?
Yes. If you blow a ring and pinion, you'll need to remove the ring gear but you will ALSO NEED to over fill the housing. Without the ring gear, there is nothing to pump the fluid out to the axle bearings and that can cause them to burn out. Kind of like the pics you posted.