Petra and the emergence of Israel

How comes that people that its national deity is YHWH name itself Israel, as if El is their God?

During most of their history, there was separation and even hostility between the kingdoms of Israel and Judah. When was it possible, on this background, for Abraham, a southern patriarch, to be adopted by E and for Jacob, a northern patriarch, to be adopted by J? If the adoption took place late in first Temple period, after the destruction of the northern kingdom, how comes that E and J developed separate traditions concerning the Patriarchs?

What is the possible history for the double, not overlapping, grouping of the Israelite tribes: on one hand tribes related to Lea versus tribes related to Rachel and on the other hand children of maidservants versus children of their Madams?

A pre monarchic hime is interwoven in Moses Blessing. In that hime God is described as appearing from four sites that are actually two specific locations. What stands behind that separation of God`s appearance?

The answer to these and other question lies in the long abode of the Israelite in Petra which is biblical Kadesh.