Group meetings are very important, and I think it is worthwhile to organise them very well, to make sure they are focussed, to-the-point, time-effective, and that everybody participates. I remember my time as a graduate student as having very efficient group meetings, and most of my points below are based on my experiences back then.
How frequent should a regular group meeting be? It depends on the field, and I hear something like daily to three months.
I think weekly is good. If people want to discuss significant results, one should not wait too long. However, too often takes away too much of peoples time.
When should a regular group meeting be? I know some groups insist on Monday morning, some groups choose Friday evening which is terrible.
I've experienced groups with group meetings on either Monday afternoon or Tuesday afternoon, and I think both are good. However, I don't think it is the most important aspect. Personally, I don't like to have meetings during lunch. Although I understand the motivation, I believe it is important to have a break from work at some point.
How long should a group meeting be?
When I was a graduate student, we had group meetings of at most one hour. We would typically have between 5 and 10 people attending the meeting (normally everybody in the group who was not away travelling). Each week, one person would be the moderator, and one person would be taking notes. Those roles would be alternating, providing everybody with useful experience in managing meetings or taking notes. We'd start with general announcements, and then everybody had the opportunity to present some plots. Some weeks, few if any people had anything to present any new results or bring up anything for discussion, and we might be done in 20 minutes. Other weeks, the role of the moderator was essential to keep the meeting to one hour.
What level of detail should a supervisor comment to one's work? From every experimental concepts, to a vague conceptual suggestion?
What I think is great about group meetings, is that it is not only the supervisor commenting. Naturally, it can happen that discussions lead into details. Although beneficial for the people directly involved in the discussion, it may be a waste of time for others. When this happens, the moderator (see above) would intervene (also in the interest of time) and suggest for a discussion to be proceeded "offline".
This hits two birds with one stone: the meeting is limited in duration, and the meeting focusses on overall discussions of broader interest.
As a student:
What should a student prepare before a group meeting to have an effective meeting? To present every problem he/she faces, or just some significant results (if there is)?
I think it is not useful to present every problem he/she faces in front of the entire group. Some problems are best discussed one-to-one with the most expert colleague (scientist, engineer, technician). But if you have any significant results — like a first version of a plot that may end up in a paper, or anything warranting scientific discussion — that can be good to show.
Should a student question other's member work? Sometimes it may be constructive, but it can also be an interruption.
Depends what you mean by questioning. I think a student should certainly comment on other members work if this is helpful. In the worst case, the comment is not relevant and the student learns something. Communication is essential to science, and communication with all members in the group has more benefits than communication exclusively between supervisor and student.