It's my understanding that when Schliemann excavated Troy, he was considered something of a Homeric fundamentalist. In other words, while he was off looking for "Homer's Troy," most everyone else in the world thought he might as well have been looking for physical evidence of a fairy tale.
On the other hand, there must have been some knowledge of the physical location of Troy, which Schliemann was able to find with the guidance of Homer and local wisdom, among the Byzantines whose territory included Ilium for so many centuries. The knowledge of Homer was fairly widespread among the educated, too. The area was fairly occupied, with Kallipolis and Dardanellia right in the neighborhood.
My question is what did the Byzantines know about the historical Troy? Are there any indications that they knew about the significance of the site later excavated by Schliemann? Were there any pilgrimages there a la Alexander the Great? Was there any effort to appropriate the legacy of the historic Troy?
Charles Brian Rose in "Troy and the Historical Imagination" in The Classical World says that the location of Troy was well known at least until the 15th century. Mehmet the Conqueror visited Troy 10 years after he conquered Constantinople and claimed that he had finally avenged Troy for what the Greeks had done. So its location was known at the end of the Byzantine Empire.
In the other direction, D. F. Easton et al. in "Troy in Recent Perspective" in Anatolian Studies claim that it was precisely the rise of Constantinople out of Byzantium that reduced Troy's significance, which prevented further development, preserving the site as an archaeological gold-mine for the Greco-Roman and Bronze Age periods.
As for the significance of them knowing the location of the 'legendary' city of Troy and your other questions, I'm not sure. Perhaps someone with more knowledge of the subject can help.