It is not easy to know Gd's will, but according to the Talmud and Mystical Judaism is it seemingly possible. It seems from most stories, that only the best of the best have even come close to this ability, though of course all of us should strive to do so.
First there are 2 main rules.**
You can never know what is Gd's will regarding other people, you can only know what is Gd's will for yourself.*
If you are in a situation where you do not have control, then by definition whatever happens is Gd's will. This is an outgrowth of rule 1. The Torah (not just the chumash) can teach us what to do in any given situation, but when we have no power to change anything, we must accept that even though this might seem to go against Gd's will if we had the power to change it, since we do not, it is not His will that it be changed, or at least changed by us.
Now, the Tanach and Talmud are large, and cover many aspects of life. Some are repeated, some go into great detail, some seemingly don't give us enough detail. There are halachot which have clear cut rules, and there agadatot which just make us think. Once we have immersed ourselves in these stories and laws we will have enough information to understand Gd's will in any given moment. (I feel compelled to add here, that sometimes you will need expert knowledge in a related field, such as farming, to properly understand what the Torah tells us when it makes use of farming metaphors or laws.)
As for the example of the two people fighting that you gave. It just so happens that we have many examples of two people fighting in our tradition when a third person could intercede. The results of interceding differed from time to time. For example, Moshe slew an Egyptian that was beating a Jewish slave, and he saw two Jews fighting and spoke to them to stop. Aharon, we are told in the Talmud would always stop two people from fighting, even lying to each of them if necessary, and for this his ways were known as Peace, one of Gd's names. (I believe there was also an incident with a prophet but I can't remember who at the moment). If a person has learned enough Torah, then when they see two people fighting, they will be instantly reminded of one of these instances by the circumstances that surround the fight. They will then recognize how to intervene. Unless I'm missing some instance in the Talmud or Midrashim or Tanach that I'm not thinking about, I believe that a person is also supposed to do their best to stop two people from fighting. Your ways should be of peace, you should always try to bring peace to others. Whatever punishments a person is meant to have, they will receive those punishments through your attempts to bring about peace. If there are sources which say otherwise, then that just means that each situation needs to be looked at more closely, and more instances of the copus of Torah integrated into a person before they can know Gd's will in these moments.
*Because of rule 1, you can be certain that anytime someone decides to make a public statement about why event X or Y happened, but they do not include their own actions as the cause of the event, or they do not include their own repentance as a possible remedy for the event, you can know that they are wrong. If they do include themselves, it does not mean they are correct, but if they don't it certainly means they are wrong.
** It has been many years since I studied this topic, and I apologize that I can not remember the source of these two rules. If anyone has heard them before and knows of their source I would be much obliged.
Edit: A thought just occurred to me. Someone reading this answer might think that you have to know all of Torah before you can ever attempt to make your will Gd's will. But I do not think this is true, you can use the Torah you do know to influence your will to be closer to Gd's will. If you make a mistake, so be it, but what you do not know at any particular moment is not really in your control. You can try to learn more on a topic before acting, but you shouldn't think that since you are limited in your knowledge that you should not even attempt to subjugate your will to that of Gd and Torah. There is a general rule in Jewish practice to do what you can, even if you can't do it perfectly, and this idea also extends from "rule 2".