Not necessarily just a sense of reference, but also a practice of always keeping in mind what direction one is when changing direction (mentally summing up the deltas in direction).

I do this when driving - I always know what direction I'm headed, even in an unfamiliar place (unless there are a ton of non-right-angle turns that confuse me, and then I have to check a map).

It's just a succinct abstraction.

Blocking a punch or doing a kata also has no concept of north. It's usually bilateral. So if you don't have left or right... Do you pretend your face is north and instruct that way?

I'm not sure what you mean. Whichever way you happen to be facing, you can use an earth-relative coordinate system to disambiguate limbs rather than a person-relative one. I guess don't practice martial arts while standing on the north or south pole and you'll be fine.

How do you explain throwing or joint-locking an opponent to someone who does not believe they have a right or a left arm? Both of these actions can involve turning around. Anywhere from 45º to 360º.