When you say "Israel" in your first point, are you speaking of 10-Israel or Judah (and Israeli Jews)?
It should be understood that not ALL of Judah has returned to the Land, now modernly called "Israel". Much of Judah still lives in the United States of America (who I consider Daughter Babylon). 10-Israelites are also in the midst of the United States. Jeremiah 50 indicates both Judah and 10-Israel would be in Daughter Babylon when she is destroyed. They will then leave weeping and looking for Zion.
Furthermore, descendants of the House of Judah and the House of Israel can be found all over the Middle East... even today. Many of them actually "think" they are Arab and/or Muslim.... or Persian... or Turkish... or Pakistani, etc...
10-Israelites have also converted to Judaism (Jewdaism) in antiquity and in modern times. So a sub-segment of 10-Israelites are hiding in plain view within the genetic Jewish population (y-Haplogroup R most notably).
The Falasha Jews are controversial of course... just like the entire subject of Judah and 10-Israel is controversial. Some think the Falasha descend from Danites. Some think they descend from Judah and/or one of Solomon's sons. Some think they descend from Levites. Some think they were non-Israelite Jewish converts. Some think they were Christian converts who embraced many Jewish-like traditions. Some think they are mixture of all of the above.
We don't really know for sure. Even in the realm of genetics, we are uncertain of the realities. Most all of the 'authorities' who interpret the genetic data are sold out to the Primary Axiom of Darwinism (and its variants) and they interpret everything from an "Out of Africa" and "extremely old humanity" paradigm.
What we do know is that the world (both new and ancient) is a much smaller place than we are generally allowed to perceive from the Darwinist cave-man worldview. The ancients traveled and mixed much more extensively than most of us are willing to give them credit for. They were NOT Geico insecure cave-men retards.
In regards, to your second point. Your family ancestry consists of thousands and thousands of branches of humanity that mixed and mingled in one of the most culturally unstable regions of the ancient world. How can you possibly "know" with complete certainty some of your ancestors do not descend from Abraham? And even if you aren't connected to Abraham physically, of course there is nothing wrong with being drawn to Israel or Judah and/or their El and His Ways.
Caleb and Ruth are two notable examples of non-Israelites being drawn to the El of Abraham, Isaak, and Jacob. Their and other non-Israelite mixing only contributes to the genetic mystery that disparate world-views are trying to unravel.
