With specific reference to Europe, would say, the Byzantine Emperor in 800 be aware of the existence of Ireland?
What would a map of the world look like to the Carolingian Emperors/kings?
I realise they probably wouldn't know or care about what was going on in those areas, but would they be aware that those places actually existed? To what extent would these maps reach?
I'm in bed so don't have sources right now but I can add them later if requested.
I completed my undergraduate thesis on the Carolingian court so will focus on that to help answer your question.
Charlemagne gathered a number of scholars from across Europe to his court, ultimately at Aachen, in his pursuit of an intellectually enlightened court to rival those of ancient Rome. One if the earliest such men was Paul the Deacon,originally from Lombardy in Northern Italy, who was of particular interest as a speaker of Greek - at the time Charlemagne's sister Grisela was betrothed to the future Byzantine emperor Leo IV, and it was hoped Paul could assist her in learning the language.
Other members of the Carolingian court included Theodulf of Orleans, a Visigoth from Spain, Alcuin of York, from English Northumbria, and Joseph Scotus, a Irishman.
Thus it can be seen that communication and indeed travel across Europe were by no means unusual in the period. One can assume, fairly reasonably given the relationships outlined above, that the Byzantine emperor would certainly be aware of Ireland, in answer to your question above. It would not be entirely unreasonable to even suggest he would have coversed with people from Ireland.
Going back even slightly earlier, it is known that Bede, on his death in 735 at the remote community of Jarrow in Northumbria, had in his possession some peppercorns, from India, and incense, from Egypt. Thus it can be seen that a sophisticated trade network existed throughout the 8th century. What I'm afraid I cannot comment on is how the world was actually depicted in maps.