Specifically where do they come from, are they "Viking" settlers of Kiev?, turkik groups? germanic peoples? overviews of them make it seem like they just pop-up out of nowhere near Bizantium's border in the 7th century.
And when did the differentiation between Western (ex. polish) and Eastern (ex. russian) slav began and what does it constitute? is it simply a linguistic divide or a deeper cultural one?
The Slavs are a ProtoIndoEuropean group, united by their shared language, which was one part of the larger Balto-Slavic branch (see here). They were neither Viking nor Turkik nor Germanic, though they share the same linguistic mother (PIE) as Germanic, Italic, Celtic, Greek, and many others (see the link). They show up in Europe in the 6th century CE, coming out of "Eurasia," the vague homeland of all the IndoEuropeans. As such, they are the "youngest" of the IndoEuropean migration waves into Europe. No one knows for sure, but I think they were driven there by the menace of peoples further east, on the steppes, like the Huns. As the Germanic peoples pushed into western and southern Europe, the Slavic peoples moved to occupy the lands they vacated (roughly NE Europe, between the Baltic and the Black seas). The sources that record them indicate they were quite populous, and quite aggressive militarily. The geographic monikers refer both to the physical geography of their dispersal (here) and the differences in their respective versions of the "Slavic" branch of the language.