Apologies for the late answer, but I've been quite preoccupied with real life issues. Let's start from the beginning here because there are a lot of questions to unpack here and they mostly boil down to understanding history as an academic discipline. You are asking us to describe the craft of an historian, which I will try to do in an understandable and succinct manner. This is actually an understanding we try to build up the first year of University education to then keep building on that understanding and to ultimately move towards more complex theories on historiography. At least, that's how it is done in most of Western Europe. I can't speak for other regions. I have limited experienced with the educational methods of other regions.

I will start by describing how history is made, recorded and studied. I will then move on to some of your more direct questions because they deserve to be answered separately. First we have to ask ourselves, how do we learn about the events that came before our own time? We do so through information that comes to us by medium of sources. Historical sources can be anything, ranging from literary documents to paintings or even buildings. Mostly historians use written sources whereas archeologists use physical remains as sources, however both are historical sources. Remember that history technically started with written history. Anything before that is known as prehistory because we lack written historical sources for that period in time and have to rely on the work of archeologists or on recorded oral history. These both have their own issues and own methodology. It's generally a lot more difficult to get qualitative information from these sources as opposed to written records for example. While this isn't entirely accurate, because for example some vases or paintings can hold a lot of qualitative information, it's mostly accurate and it's why these sources aren't considered the core source material for historians. Still, historians can obviously also use oral history or physical remains to supplement their research. It's not a clear cut division, but it's a distinction worth pointing out. The first written sources are generally considered as the start of written history and thus also the academic discipline of history.

So now we know what historians need to do their research. The next question is : "How did these written sources came into being and why should we believe anything they say?". This is a concept that once understood will answer most of the questions you asked. Let's start with why we should believe these sources. Well, we shouldn't. That's a major part of being a good historian. Historians have to take into account why a written source was created and by whom it was created. The information presented in a dramatic recount of an epic battle written at the request of a noble who was involved in said battle, is far less likely to be truthful than the information we find in a document that was created purely due to practical concerns - such as a will or financial record. That doesn't mean that that the former is less valuable, far from it. Cross-checking the information found within this recount of the epic battle with different written records of the same event can not only tell us something about the accuracy of the information within these documents, it can also help us understand how this battle was represented and maybe even why. We could for example deduce that specific parts of the recount written for the previously mentioned noble were purposefully enhanced to paint him in a better light. This is obviously an oversimplification, but this type of analysis teaches historians a lot about the culture and written tradition at that time. Knowing how someone writes and why he does so, says a lot about the culture they are a part of. This is why the information available in historical records which were written purely out of practical concerns, isn't more valuable. It's just different information. Mostly these more practical documents will feature more "quantitative" information whereas less practically oriented documents will have more "qualitative" information. They require different types of analysis and are both important parts of historical research.

These are the very rudimentary basics of how history is made. Historians then research the information present in these sources and try to make a convincing narrative for what they believe to have been the historical reality at that time. With historical reality we mean what actually transpired, how did they process it and how did they see the world. Things like that. The narrative made by the historian is then published and reviewed by other historians. It is then refined, accepted or denied through other research. When that narrative becomes widely accepted as the historical reality of that time, it becomes the academic consensus. It's this academic consensus that turns into history lessons at school and makes up "historical facts". This is important to note because within academia, facts aren't locked in. They are subject to change whenever new information comes to life or when these widely accepted narratives are no longer accepted by most prominent historians who are knowledgeable on the subject.

With all of this in mind, lets move on to some of your questions :

Why do people keep history? What I meant by this is, is there more reasons that I'm not seeing or thinking very well? I'm not that smart. One of those reasons is, or the simpler version, is to know what not to do in certain situations. To not forget about them, preserving knowledge from the past. Is there more to it?

Like I said in the previous paragraphs, there are many reasons as to why. Sometimes it's purely out of practical concerns. Sometimes it's a vanity project. Sometimes it is to share an experience with contemporary readers. Sometimes it's purely due to the desire to write something down. There are many reasons as to why written sources are created. It has to be noted that diaries are actually quite rare in many cultures and time periods. The idea to write purely to express oneself without an audience wasn't always common.

The phrase, "those who don't learn from history, are doomed to repeat it", did someone experienced this? If yes, then how many times did it happen?

This statement is technically false. It sounds good, but it's not historically accurate. We can draw comparisons between different time periods, but history will never repeat itself. There are too many variables and even if by some divine cosmic coincidence history would repeat itself, the repeated events would still be distinctly unique simply due to the fact that our perception of time is linear. So the fact alone that they are separated through time and space makes them not identical. However, what this expression does imply is that there are a lot of lessons we can learn from history to form a better path towards the future. This much is true in my opinion. That's why I am very passionate about history being a crucial part of every education, even though it currently usually is not. When we understand where we come from, how we got here and what we did wrong, we can more easily navigated towards a brighter future.

We won't repeat past mistakes - at least not with the exact same context -, but we can learn from them. I hope this helped!