Well, it's hard to answer those questions simply, because there's a lot we don't know.  But we have seen some features that bear out these historical claims:  The Shang was certainly historical, and the Shiji reports its royal line with fair accuracy.  The Xia may or may not have existed -- certainly something large predates the Shang, growing chiefly out of Longshan culture.  As for whether Longshan and Yangshao cultures represent the peoples of the "legendary" sage kings -- it's hard to know what to say:  certainly, these were impressive Neolithic cultures, and some members of these cultures must have made great contributions and played leadership roles, but whether the legends of the sage kings recall actual leaders, or are rather, perhaps, recollections of local deities, whose names we may see preserved in the oracle texts, is an open question.

What we have seen is that the society that we call "China" evolved over a very long period of time, drawing on a mix of cultural sources.  Next meeting, we'll make a final survey of the latest stage of that evolution in the pre-Zhou period -- the society of the Shang, as we see it preserved in the remnants unearthed near Anyang.