During and after the talks and seminars in our dept. (~80 people, ~10 groups, ~40 postdocs+PhD+Master students), it is extremely rare to see postdocs or students asking questions. 90-95% of the questions are asked by senior people (mainly PIs or experienced permanent researchers).
My first thought is that this a large group -- maybe too large. In my department (mathematics, at a big US research university) if you count tenure track faculty plus postdocs plus graduate students you get about 100. For this group of 100 people we don't have one research seminar, we have 8-10 different seminars. (We do have a departmental colloquium, but not so often -- in part, I think, because the people who want to go to see talks already have plenty of talks to go to.) I am a number theorist, and I feel a very high degree of "mineness" about our number theory seminar: I spoke in it today, as I do once a semester. I gave a ridiculously long talk (90 minutes -- hey, that's what we're scheduled for) and most of the core audience stayed until the end. When I miss a single week of the seminar, people ask after my whereabouts and well-being. There are several other seminars in my department of interest to me, and I attend when I can -- but they're not mine in the same way. And by the way, I am a tenured, full professor who has spent 20 years cultivating a broad, shallow knowledge of many different areas of mathematics, but for almost half of my department's seminars I would be too lost to want to attend regularly and too lost to ask good questions. Math is indeed hard, but so are other academic fields: I am really skeptical that all 80 people are equally invested in any one talk.
I would suggest scheduling more and smaller seminars, both dividing by research area and also by seniority. Can a talk really be pitched equally at senior faculty and students? This seems very unlikely. In the talk I gave today, I decided to pitch part of it at the students much more honestly than I often do. So perhaps the first 15 minutes (of 90) were truly aimed at them. The rest was aimed at faculty (including postdocs) and indeed the largest number of questions came from the most senior person in the room. More or less we are expecting that to happen by collecting that audience. Students are still there and still getting things out of the talks -- for instance, one of my PhD students attends the number theory seminar as faithfully as I do. Only very rarely does she ask questions on the spot -- but we often discuss the talks afterwards. She is also active in organizing the Graduate Student Seminar in my department, in which faculty are allowed but not encouraged to attend and usually do not. In fact, I had a period of about one year where I often attended the Graduate Student Seminar, but I stopped going when I realized the extent to which my presence there was warping the proceedings in a negative way.
In fact, here is a parable from when I was a graduate student. One of our seminars, the Basic Notions Seminar, had once upon a time been the "Graduate Student Seminar." But it was the kind of graduate student seminar where the faculty would give talks -- nice talks, which other faculty members would attend. After a while the students realized they needed their own "Graduate Student Seminar." They gave it a name -- the Trivial Notions Seminar -- which made it clear and obvious that faculty were not wanted as speakers or audience members. Both seminars have coexisted for many years.
We want to find a way out of it. One possibility under discussion is to force, right at the end of the talk, the first couple of questions from them. But it's not accepted yet. Do you think this could be a good idea?
It could be a good idea, but I don't recommend it. There are probably many reasons why young people are not asking questions. As you made clear, young people who do have questions do not feel fully comfortable asking them. If you want to address the issue, then actually address the issue by creating an environment that makes them more comfortable. Forcing them to ask questions seems willfully dismissive of the reality that they are uncomfortable, which they probably actually are. As I said above, one of my students faithfully attends my seminar and rarely asks questions. If it were my choice, I suppose I would rather she ask more questions. But it obviously is not my choice: she is a thoroughly intelligent, competent, professional adult person, and one whom I know well enough to understand and respect why she behaves as she does.
Rather, I think that if you want students to ask questions, you need to actually create a seminar environment in which this is what they'll naturally do. I gave some suggestions for this above in terms of who is in the room. There are many other things you can do, if it is important to you. One big one is to get speakers for whom interacting with the young audience is something they want to do. When I teach graduate courses I get lots of interaction from the students, even though some are not so comfortable asking questions. How do I do this? By saturating the lecture itself with questions and interactions with the students. I will literally ask for students to complete my sentences. If I need to make a definition, I will say "Someone must know this" and ask a student to supply it. If the student gives the definition in exactly the form I want, I write it down quickly and we go on. Any discrepancy gets incorporated into the lecture on the spot (and is not necessarily bad or problematic: there are many different ways of saying the same thing, and what could be a better use of class time than showing a student that the thing they have in mind is actually the same as the thing I have in mind, or should be the same except for one technical point they have missed...) When I give a seminar talk, I still try a bit of this kind of didactic Q&A...but it depends on what the audience wants. Sometimes every single question will get snapped up by the people who know everything. Sometimes people will say nothing and not look me in the eye, trying to pretend they know the answer. Sometimes they will say nothing and look me in the eye, trying to get me to get on with things. In my home seminar, the senior people will play along with me if they clearly understand the game we're playing...but in part because they know I'm mostly pitching things at them.
One final idea: you can keep the seminars entirely as they are now -- again, please understand that the senior people are probably largely happy with them -- and add an additional component afterwards which is just for the junior people. Or talk to your junior colleagues, find out what they want and what environment would make them more interactive, and see if you can create that environment. But don't force the issue, and don't assume that everyone will feel the same way about it that you do.