Really? I'm yet to meet a single diaspora (i.e. born/raised abroad) professor here in Korea and I interact with universities quite a bit.
Unless diaspora here includes those who did their full university education abroad though, lots of those indeed.
Yes. By definition these are diaspora members as well.
For what it's worth, I've really never seen pure international students really been included in that term, especially those that are the student equivalent of expats on a fixed-term contract - another group I've never seen included. In all discussions I've been part of, it' s about people with heritage from country A (whether born there or through family), but "settled" (or if a minor, being raised) in country B, with the above two groups not fitting into the "settled" part, planning to move back to A the second their contract(/term) ends. But I'm sure there's other valid definitions out there and it depends on the context and all.