So, I am currently writing some stories that are heavily influenced by King Arthur, the Round Table, etc. But during my research about the subject, I didn’t found specific dates regarding when the events of the Arthurian Legends could have happened.
I have read that the historical version of King Arthur was a Roman in the 5th Century, I also heard that he could have existed around the 9th and 10th centuries.
Then I asked my history teacher in college: She said that, if King Arthur existed in the way the legends depict him, it should have been somewhere between 1200 and 1400.
What do you guys think? Which dates could be the most believable and historically accurate?
The answer to your question is Yes. Whatever you want. I had an Arthurian studies professor once tell me that there were 5,000 sources mentioning Arthur dating before 1500. I don't know if that is true, but there is no question that there are hundreds and likely thousands of Arthurian sources throughout time, and they span the full range of possibilities with regard to the "when" of Arthur.
People often look for "proto-Arthurs" in the fifth of sixth centuries, looking at British warriors who perhaps retrained something of the Roman world that departed, fighting against the Anglo-Saxons who were arriving.
Actual Arthurian literature tends to place it in a former romanticized time, but these authors at the same time project a great deal of their contemporary culture into that romanticized time. That process tended to be "locked" by the the fifteenth or sixteenth century, by which time contemporary influences ceased to be projected backwards (one does not find Arthur's court to be much like Queen Elizabeth's, by which time, a medieval cap was placed on the Arthurian world and it fossilized as medieval to a certain extent.
In that sense, your history teacher is correct: the literature tends to depict Arthur and his court as being somewhere between 1200 and 1400 - even as historians look for the "real" proto-Arthur in a much earlier time.
The first reliably dateable mentions of Arthur are ninth-century, and they place him c. 500. I think what your history teacher meant was that the setting of the Arthurian tales seems much more high medieval than early medieval (this is basically because so many of the stories developed at that time and reflected contemporary realities and ideas). Arthur wouldn't have been a Roman; though a leader at that time would probably have had some knowledge of Latin and would have used (late) Roman-style weapons and armour.
The problem is that even the earliest sources on Arthur are pretty unreliable, and their material on him seems to be of poetic origin, rather some dry historical record. Some of the information seems to be very clearly false (it appears that there was a tendency to ascribe any famous battle to Arthur). Many historians argue that Arthur is an entirely legendary figure, though personally I belong to the 'no smoke without fire' camp. Nonetheless, I think that the only thing that we can be even fairly sure of is that there was a prominent British military leader called Arthur who lived in the fifth or sixth century.
Here are online translations of the two ninth-century sources, do ask if you want me to go into more detail.