Yes it is arbitrary (like most of things actually) but the distinction between Europe and Asia is the most arbitrary of all of them

It's an interesting topic since most people in a hypothetical Eurasia would probably never call themselves Eurasian, but would have a strong sense of being one or the other. But on the other hand there is also no universally agreed to boundary between the two as well. And maybe this imprecision the best representation of reality that we have for this.

That'd be another definition we could use yes