Wild. My layperson mind goes to a simple example, which may or may not be possible, but please tell me if this is the gist:
Alice and Bob, in different reference frames, both witness events C and D occurring. Alice says C happened before D. Bob says D happened before C. They're both correct. (And good luck synchronizing your watches, Alice and Bob!)
That will be the case when Alice stands close to where C happens, and Bob stands close to where D happens.
It's a little trickier to imagine introducing cause-and-effect though. (Alice sees that C caused D to happen, Bob sees that D caused C to happen).
I think a "light cone" is the thought-experiment to look up here.
Yes that definitely happens. People orbiting Polaris would be seeing two supernovas explode at different times than us due to the speed of light. Polaris is 400 light years away so the gap could be large.
But when you are moving you may see very closely spaced events in different order, because you’re moving toward Carol but at an angle to Doug. Versus someone else moving toward Doug at an angle to Carol.