Could DNA prove this?
I am not sure what race the 12 lost tribes of Israel are? proably semetic...Can white people or Indian people be semetic?
DNA can. There have been extensive DNA studies done on Jews from Europe, Asia, Africa, and the Middle East.
This was done because of claims made by Arabs that the Jews returning from Europe to Israel were not descendants of ancient Israel.
The DNA study showed that there are definitely links between European Jews and the Middle East, even after so many centuries of Diaspora.
I'm not sure.A few years ago,there was a DNA study of a black African tribe's "priests"/rabbis,And yes,they shared the same DNA as men whose last names,all over the world,are Cohen,Kohn,and other variations.These men are all descendants of the "priestly class",from ancient times.
Yes it could.
Sure DNA could prove this. I imagine that if the calim is true, they are related to either Persian and Central Asian Jews, or to Yemeni Jews. I doubt that they are one of the lost tribes. Personally, I believe that this distinction belongs to the Kurds.