a) If I'm paying for a lesson, I wouldn't want to wait more than 5 to 10 minutes without any previous message unless the time can be extended. For example, if the teacher is going to be 15 to 20 minutes late but offers to extend the lesson 15 to 20 minutes beyond the ending time, and if I don't have a previously scheduled appointment, I would be okay with that. If the teacher has back-to-back lessons, this may not be possible. In that case, I would want to reschedule the lesson or receive the credits back.

b) Before italki changed their policy, I was more strict with new students showing up late to a lesson. I know life happens, but time is valuable, and new students needed to prove their punctuality in the first lesson. As a tutor, I may be a couple of minutes late from time to time, but I take punctuality seriously.  My policy was if a new student showed up 10 minutes late without prior notice, they'd forfeit the credits. For returning students, since they've built a rapport with me, I've always been a bit more lax about it. Now, of course, I'm required to wait since the policy changed. Fortunately, I haven't had too many problems since they changed it.

c) For a free language exchange... I guess it would just depend on my mood and how long I want to wait, or if I have other appointments. If I feel like doing something while I wait, I'll do so. If have to get to my next appointment soon, then I'll wait and do something to pass the time until there's no time left.