1. Chairing a panel at a conference, in response to a general "call for chairs" at a conference organized by one's supervisor. Not an enormous conference, more of a regional thing but sub-field-specific.
By all means. As a grad student, I put things like this under "Service to university community and profession." (I've since split into two.)
2. Giving a talk to other grad students about strategies for writing particular grant applications based on one's experience as a successful applicant. It was a guest lecture in a mandatory course—kind of a "Grad School 101" thing.
If you're not a student in the course, then I see no problem with including it under service to your department or university--as long as you didn't have to do it. If you're a student in the class, then I vote "no."
The latter I would like to put on because I've done a fair bit of mentoring of grad students who are earlier along in the program than I am and I would like to make this apparent to search committees when I go on the market, but I'm not sure if I should make it a line or ask one of my referees to mention it.
It's highly unlikely that you will be interviewed or hired due to your involvement in mentoring other graduate students. It's not a bad thing, but it's just not going to carry that much weight.