Several Questions.

[Mulceber]

It depends at what point of its history the kingdom was referred as Syria. Eventually the Seleucids ended up only with Syria. But even before that their core regions were Mesopotamia and Syria. Their rule in Asia Minor and Iran was never strong and consistent. Culturally they were closer to the more Hellenized population of Syria than to more "Eastern" population of Mesopotamia.

I'm by no means an expert, so I can be wrong, so any corrections are welcome :)

Also, this is just conjecture, but since they didn't have consistant power in Turkey, that means that the only area in which they consistantly had access to the Mediterranean was in Syria/the Levant. Roman and Greek sources are where much of our information on this comes from, so if the only area where the Seleukids touched the mediterranean was the Levant, that's what they would be known for to Greco-Roman writers - as Syrians. So they could be known as such strictly because that's what the Romans and Greeks knew them for. I'm not saying the Greeks and Romans wouldn't know anything about the east (that's definitely not true), but the Levant would likely be the area of the Seleukid Empire that they were most familiar with, and thus how they identify the Seleukids, even though they controlled far more than that. Again, this is just conjecture and I could well be wrong. -M