Just wanted to confirm with the community - is this shifter - Shimano XT SL-M8100 12 Speed (link below) Compatible with my all XTR setup?
(Groupset Shimano XTR 9100 12spd)
Shimano XT SL-M8100 12 Speed Shift Lever
Also - my current shifter appears to have died, it works as normal - but once you shift to an easier gear the big lever just goes all floppy and 'dives'.
Then after 5 seconds or so it's all back to normal with the lever stiff and clicking. Rinse and repeat.
Shifting to a harder gear always works as per normal. Is this fixable in anyone's experience?
cheers and thanks 
Shimano stuff from the same "generation" is cross compatible. So XT 8100 is compatible with XTR 9100. So on and so forth. Compatibility between generations gets a lot shakier. Some is, some isn't. Depends on exactly what Shimano changed between those generations.
As for the Shifter behavior, that's extremely common for Shimano stuff with lots of use/wear. Usually the first signs of it will only appear in subfreezing temps. But then when it warms up, everything works fine. It is at least in part caused by the lubricant Shimano uses getting gummy and causing the mechanism to "stick". This lubricant becomes gummier when cold. I once saw a guy's Shimano freehub do this. Pawls wouldn't catch when he was winter commuting (was probably -20F outside at the time). Brought his bike inside and in the few minutes it took for us to get it on a stand, the bike had warmed up enough that the pawls would engage again.
When this happened to a shifter, we could revive it for a time by spraying an aerosol degreaser such as Clean Streak into the shifter through the cable install port. Give it a good soaking and then blast everything out with an air compressor nozzle. Lubricate with a light chain lube such as triflow and it'll work again for awhile. At least until the other factor becomes predominant, which is wear of the plastic bits inside the shifter mechanism. They'll eventually give it up and you won't be able to recover the shifter with the clean/relube method.
I've seen this happen on Shimano's full range of shifters. All of their trigger shifters from the cheapest Altus all the way to XTR as well as all of their drop bar shifters. Ride the bike enough for the lube in there to get gummy and you'll experience this. Happened to one of my own bikes once, too. Usually takes awhile, though. For me, it took more than a decade on the same Deore 9spd shifter, but I guess if you ride a ton, you can destroy that grease in less time.
