I am very interested in this specific question, but if someone could refer me to reliable sources about historicity of the bible in general, that would be a great addition.
Whole careers are devoted to the historicity of the bible. I leave that subject to others.
Yes and no: while many biblical passages about camels are historical fantasies, they're off by a millenium or less, rather than "thousands of years". More specifically, it's now common to date Abraham to some time between 2200-1800 BC. Domesticated camels appeared to proliferate in the Levant around 950-900 BC. So for a Mesopotamian migrant to Canaan to rely on pack-camels during his travels around four thousand years ago ... well, it just doesn't fit the evidence we have.
Dating of the Patriarchs is itself a centuries-old enterprise. The "Nova" television program says a few judicious words here about the legendary Abraham.
Camel domestication is remarkably recent, quite distinct from that of other quadrupeds, and a topic of ongoing research. Four years ago National Geographic nicely summarized recent research focused on arrival of domesticated camels in ancient Palestine.