Yes, it'll be in the next update (ETA unknown).
It won't.
Everything about the plane itself is compatible (bugs not withstanding). It's only Gizmo that isn't.
Unfortunately any time that X-Plane does the "loading flight" screen it resets the livery to whatever you selected on the initial flight configuration. You could consider reporting that as a bug to LR. *shrug*
I would sometimes do this so I wrote a script to maintain the time at which I paused the sim when resuming. https://github.com/pilsnerish/FlyWithLua-Scripts/blob/main/PauseResume.lua
There's nothing particularly special about how the CL650 reads the Throttle 1 & 2 axis values, as long as they're assigned in X-Plane. But this assumes the throttles aren't being held down by the red locks, or some other binding.
Most other developers just use the default system and call it a day. Hot Start will do it 100% custom to match the real world equipment.
Not sure what you "fell for" considering no where does it say the add-on includes a weather radar. ¯\_(ツ)_/¯