There is no central authority that regulates anything. Each journal and each conference have their own policies about such things. In any case, it is not in general true that in computer science "a journal paper cannot be presented in a conference because of plagiarism reasons, and viceversa". My answer to another question explains more about the difference between conference and journal publications and how they interact with each other (the answer is not area-specific, but it was informed by my specific knowledge of computer science publication conventions).
As for your other questions, they are a bit vague but I'll try to answer them:
I have had multiple arguments with colleagues of other fields that
disagree with me (I am in a multidisciplinary field). I feel I tend to
lose these argumentations; and basically nobody really believes me
because I would need a bunch of people in my field as proof.
If I understand correctly what it is that you are claiming in your arguments with your colleagues, it sounds like they may be in the right. However, it's a bit unclear what your position is precisely, so perhaps you should try to clarify that.
If I simply don’t want to follow the rule, what are the real
consequences apart from the social lynching. In a multidisciplinary
field we are already kind of being punished when we hear that
conference papers don’t count as publications. Is there any way to
confirm that a conference or proceeding is formally registered as an
(or to an) editorial/publisher?
Again, I'm not sure what rule you are referring to. As I said above, there is no centrally regulated system of rules. Each journal or conference will have their own publication policies which you should comply with. These are not "rules" in the sense that disobeying them will get you arrested, but not complying with these policies will quickly get your papers rejected and/or get you labelled as a dishonest or unethical researcher. If you are after an academic career, it is completely counterproductive to do this, and if you don't want an academic career, I don't really understand what would be your goal in trying to work around the publication conventions in such a way.
Is there any other way of presenting published results in a conference
as, for example, simply abstracts?
Again, I disagree with your premise (at least in the generality in which it is stated) that one cannot present published results in a conference. I'm in math rather than CS, but I have done precisely that many times (Edit: to clarify: in math, conferences usually don't publish proceedings, so "presenting" does not equate to a publication). Even in many CS conferences, you could do that by taking care to first submit an extended abstract version of your paper to the conference, presenting it there, and following that up with a more detailed paper which you will submit to a journal. The order does matter, as the answer I linked to above discusses, but that's the logical order of doing it anyway, so I don't really understand what the source of your frustration is. If you add more details to your question I'll be happy to discuss them.
Edit: Here are some more thoughts addressing the very helpful clarification comments you left below my answer.
I sympathize with your money issues, but honestly you are mixing two completely unrelated things here. The fact of the matter is, publishing in a journal first and then in a conference is less logical and rather defeats the entire purpose of the system of dual conference-journal publications (and, to be clear, I rather dislike this system myself and think it has some serious flaws, but it does have a certain logic to it, which you are trying to work against because of the unrelated money issues).
What I think would make sense for you to do is to determine what is the optimal way to publish your research from a scientific point of view, ignoring the funding issues, and then go to your advisor and/or department, explain the problem to them and ask them to help you achieve that goal. If they are running an honest graduate program, it is their responsibility to provide grad students with the resources they need to succeed in their work. So, I think that problem ought to take care of itself if you go about things in a mature way instead of trying to work around the system, flawed though it might be, and ignore well-established conventions in your field.
As for "conference papers don't count as publications", that statement simply does not have a well-defined truth value, and in fact, I think asking questions like whether a conference papers "counts" or does not "count" as a "publication" (whatever that is) is misguided and unhelpful. Here's what in my opinion is a more helpful way of thinking about this topic: a conference paper is precisely what it is, nothing more or less - it is a form of publication that has certain characteristics in terms of the rigor with which it was evaluated, the level of certainty that it is correct, etc. When you are evaluated by others in connection with job applications, promotions, etc., it is important that they understand the context for your achievements so that they can reach an informed opinion about how good your work is. When working in a multidisciplinary field, you are correct that there can be a risk that the people evaluating you are not sufficiently informed about the conventions in some of the fields you are working on to have that context. I agree that this can be frustrating and worrying, but I think there is only one correct way to address this concern, and that is to provide that context in an honest, clear, concise and readable way in your CV and other documents (research statement, publication list). If your department is unfamiliar with CS conference proceedings papers and how much they "count" for, explain to them what such papers are about; e.g., have two sections in your publication lists, one for journal publications and another for conference publication, and include a small footnote to explain the distinction.
On the other hand, do not be tempted to try to game the system in any way, by, for example, withholding that context, trying to pass off a conference paper as a journal paper, ignoring editorial policies of a journal or conference you submit to, or any other means that can be viewed as dishonest or unethical. That will only lead to trouble.
To summarize, I understand from your comments that you have some legitimate concerns about funding travel to conferences and about having your work be evaluated by people who do not understand publication conventions in CS, but it seems to me that you are contemplating some rather ill-advised means for addressing those concerns. Academia is not perfect and one often encounters such less than ideal situations in almost every discipline, but I find that a little bit of creative thinking, maturity and honesty will almost always overcome them.