I may be unusual in this regard but I don't think I can remember a single time that I have fallen asleep "by accident." I've never been able to fall asleep in class, or reading a book, or watching a movie or just lazing about the couch late at night. Is this something most people have to worry about?
It's not something I worry about (since sleeping is great) but yes, I can sleep pretty much anywhere I'm comfortable. I can't easily fall asleep if my head isn't supported though so falling asleep when sitting upright doesn't really happen. The thing about the method discussed in the article is that your head is always supported so yeah I could imagine myself falling asleep during a long conference call (if I wasn't engaged in the material).
Absolutely. When I had a workout (or went running or hiking) on the same day or even the day before, it is extremely hard to keep my eyes open after 9:30pm. I could be watching / reading the most exciting thing.
When I "just work" i.e. don't do much in terms of physical activity, I can stay awake as long as I want.
I've fallen asleep in class, during exams, reading a book, watching a movie, having a conversation, sitting around in a living room, etc. I think it just kind of depends. Some people fall asleep easily anywhere (ironically I cannot sleep well in beds), other people do not.