How to conduct an effective regular group meeting?

You have a lot of questions interspersed within your question, but it sounds like the main issue is

the research area of the group is very diverse, every time I just listen on something I cannot understand and have totally no interest on it, and I believe other members think the same way as I do when I am presenting.

I have had the same problem in the past. I'm a professor who works in a variety of related subfields, some very theoretical and some fairly applied. Most of my students and postdocs have been focused exclusively on either something theoretical or something applied, and their backgrounds range from computer science to mathematics to electrical engineering, so there is often a disconnect when they try to communicate what they are doing. Here is my advice.

For students:

1. Try to broaden your focus and interests. It is natural that you have a very narrow research focus as a grad student, but if you want to get and keep a job afterward you'll almost certainly need to broaden your focus. I find that in general the best researchers almost always have broad interests (though they are able to focus their energy narrowly when needed). Group meetings are an opportunity to become acquainted with topics that are on the horizon of your current knowledge.
2. Use group meetings as an opportunity to improve your communication skills. Teaching non-experts about your work is a critical skill in any research career. Other students in the group do not know nearly as much as you about your research topic, but that doesn't mean that you cannot make it interesting and accessible to them. Often this means leaving out the "details" and explaining just the essence of a problem. Trust me, some day soon you will need to make your work interesting and intelligible to people who are much further removed from your specialty.

For advisors:

1. Help students to present their work in a way that the others can understand. Often this means prompting the student, especially at the beginning of a presentation, to add important assumptions, motivation, or background. The student has started to take these things for granted, but without them any non-expert is quickly lost.
2. Don't let the conversation drift too far into a very specialized discussion. If you and the student are the only ones who have any idea of what is being discussed, it's probably time to say "let's discuss this further after the meeting".

3. Use meetings for skills development. This was already mentioned in this related answer. Instead of focusing exclusively on research, group meetings can also include discussions of things like:

   • How to write papers
   • How to read papers
   • How to search the literature
   • How to manage a bibliography
   • How to give good presentations
   • How to write a proposal
   • How to keep a lab notebook
   • How to keep up with newly published research
   • How to stay organized and be productive
   • How to referee a paper
   • Software tools for all of the above, and for research

These topics are useful and interesting to anyone involved in research.

Answers to other parts of the question

• I hold group meetings once a week, and they last 1-2 hours
• Students are strongly encouraged to question and comment on each other's work
• We meet at lunch time, and there is food. That doesn't sound important, but I think it is.
• I try to save very detailed comments for my one-on-one meetings with students. Otherwise, the group meeting can devolve into a conversation between the advisor and just one student.

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.

1. As a participant, and this applies to all kinds of meetings inside and outside of academia, it depends on whether it is a structured or unstructured meeting. It also depends on whether it is instructor led or student led. In both cases, having an agenda for the meeting will make it more effective; more on this below.

2. If the purpose of the group meetings is to brain storm in a collaborative environment, examine each others work, offer insights from unbiased but informed perspectives, and generate discussion, then an unstructured format is generally preferred. This gives participants the freedom for expressing ideas that may have a limited time value and impact. But this is also only valuable if there is a moderator to step in and control the discussion, allocate time to the points to be discussed, and everyone is a participant. If no one is, then there is little value to holding the meetings. The most effective way to create the agenda for this, as well as determine the length of the meeting, is for the moderator to poll the participants on what points they wish to discuss. This can be during the last meeting, prior to the meeting through a communications medium, or at the beginning of the meeting. In all cases there should be common agreement that the agenda, once decided, is fixed and that all other discussion points will carry over to the next meeting if they are important enough. Time wise, it should be reasonable; only an hour or two at most. More than that and you start to suffer attention span attrition. Frequency is based on need; if there is no need, then there should be less frequent meetings. But I will not say that there should be no meetings; because that would signify that all of you have no interest in socializing with your peers, and do not consider peer and instructor review valuable. Which would not be beneficial from a professional standpoint.

3. If the purpose of the meeting is for everyone to present current findings and receive pointed guidance, then a structured meeting is preferred. The agenda is based on who has something to present; which all of you should, even if it is only current actions undertaken in your research. The danger of structured meetings where everyone is a participant, regardless of inclination or material, is that they can be extremely long if there are a lot of presenters; and also tedious if there really isn't anything to report and they are filling white-space. The easiest way to create the agenda is to have a roster of the group and to have them brief their findings in the order that they are on that roster. They each have a set time to give out their information. The instructor then gives his guidance and possibly polls the group for opinions. Then the groups moves on to the next presenter. Structured meetings with definite presentations require some legwork in the background. The most efficient way to get through multiple presenters is to have all of the presentations consolidated to one computer, either merged into one slide deck, or organized by briefer in the same folder. Who does that is something I'm sure the instructor will notify all of you about. Time should be based on how many are in the group.

4. There are pros and cons to both approaches. The effectiveness of either depends on the participants and the instructor. If your meetings are not effective for any of the participants, then maybe you need to suggest to the group (off-line, during, or private session with the instructor I leave to your discretion) that the point of discussion for one of those meetings should be the effectiveness of those meetings. And then determine what each of you individually needs to take away from it, as well as what ways you are all collectively going to improve the quality of those meetings.