Is there a DNA test that is more precise in determining if a man with haplogroup J-P58 gentically stems from either Arab or Jewish descent?

Answer 1

Jews don't carry adequate amount of J-P58 unless they descended from Yemeni Jews. All Jews who came from Middle East (Except for Israel) have similar genetic make up except for Yemeni Jews. Yemeni Jews are predominantly Arabs in genes (J-P58). The other Jews have less than 1% of J-P58. Most Jews are more related with the people of Levant through the portion of haplogroup J2.

Answer 2

Yes. Compare his entire DNA to that of his parents, that of his parents to that of his grandparents, that of his grandparents to that of their parents, etc

A haplogroup by definition is just one of your 47 traceable bloodlines

Answer 3

It gets too tricky at that point to reliably determine