Concerning the issue of the term Ivri vs. Hapiru / 'Abiru. It is clear that the term Ivri (עברי) / Ivrim (עבריים) is how Jewish texts describe Avraham ben-Terahh his children, grandchildren, and further who kept the mitzvoth that he did, in the way he did. I.e. one perspective is that this term, as it is pronounced in the Tanakh, was an internal term to Avraham's family who followed in his path.
With Hapiru / 'Abiru it isn't "historically" clear that these terms were used specifically to describe the Ivrim (i.e. Avraham ben-Terahh and all who followed his way of life). What is clear is that "historically" the terms were more general to describe various people who where from regions in and around Canaan, Moav, etc. and the Ivrim, and eventually the Benei Yisrael, were possibly grouped into these term for conviience since they were in the area of Canaan and beyond.
I.e. not all Habiru / 'Apiru were Ivrim / Benei Yisrael and possibly in some situations Habiru / 'Apiru was used to describe Ivrim and Benei Yisrael.
