With all due respect, I think there's a little confusion here and mixing of "labels"...
Abraham was not a Jew. Abraham was Ivrit, which translates to Hebrew, which means "of the other side" (there is some speculation on the etymology of the word Hebrew, possibly Greek or Aramaic). He was a missionary of sorts and convinced others of the Oneness of G-D, and these "converts" became monotheists, aka Hebrews, also.
Some scholars believe that Hebrew is a reference to the fact that he was originally from Ur, left there and settled on the other side of the river... and then there are some scholars that believe it refers to the fact that all those around him were polytheists and Abraham believed in the One G-D - a spiritual distinction, if you will... and then there are those that believe it is a combination of both. Abrahams wives were also monotheists aka Hebrew, as were his children.
His son, Isaac, was also a Hebrew, as was Isaacs’s son, Jacob. Jacob and his wives, Rachel and Leah and their handmaids continued to believe in the One G-D and passed that belief onto his children. Jacob wrestles with an Angel throughout the night before he is to see his twin brother Esau for the first time since receiving the blessing from their father and is renamed Israel meaning "One who wrestles with G-D" - and while his name seems to be interchangeable throughout the Tanakh some scholars hold that when Jacob is referred to as Israel, it is reference to his spiritual being .
Jacob/Israel has 12 sons whose descendants become known as B'nai Yisrael or the Children of Israel. The sons of Jacob/Israel have children and it is by these sons names that the Tribes of Israel are identified: Asher, Benjamin, Dan, Gad, Issachar, Joseph (Ephraim & Manasseh), Judah, Levi, Naphtali, Rueven, Simeon, and Zebulon. However, the descendants of Jacobs sons aren't referred to as Israelites until about the time just before the Exodus from Egypt. The Israelites are monotheists and believe in the One G-D of the Patriarchs and Matriarchs, Abraham, Isaac and Jacob, Sarah Rebecca, Rachel and Leah.
It isn't until after King Solomon, when there is a political break between the northern tribes and southern tribes that the [i]label[i] identification begins to change. The northern tribes, comprised of Asher, Dan, Gad, Issachar,Joseph [Ephraim and Manasseh], Naphtali, Rueven, Zebulon and the Levites living in the priestly territories in the north, are referred to as [i]Israel [i]and the southern tribes - comprised of Judah, Benjamin, Simeon and the Levites whose priestly cities are located within the southern territories.
The southern tribes merge into one and are known by the largest of the these, Judah. The territory that Judah occupies becomes known as "Judea".
After the Babylonian exile the northern tribes disappear thusly and become known as the 10 lost tribes of Israel. Judea returns and eventually the Judeans become known as ... you got it, Jews -
As for "who is a Jew?" Anyone born of a Jewish mother is considered a Jew, period. Tribal affiliation is through the father, spiritual affiliation is through the mother.

As for Isaac, information on him is thin. He was borne to Abraham and Sarah when they were quite old and there are some scholars that believe he had Downs Syndrome - but of course that is speculative. Biblical scholars put his age somewhere between 36/37-42 when the Akedah, the binding of Isaac takes place. We know he never sees his parents alive after this event. His mother, Sarah (also a Hebrew), passes away when she learns the details of Abrahams journey to Moriah. And while Abraham arranges a marriage for Isaac, he, Abraham, does not attend the festivities. When Abraham dies Isaac and Ishmael come together, unite as brothers, to bury their father.
Isaac and Rebecca go on to have twin sons, Esau and Jacob. Isaac favors Esau and Rebecca favors Jacob. Isaac, in his old age, goes blind. While lying on his deathbed he calls for Esau and asks him to make a favored meal. Rebecca overhears, makes the meal and convinces Jacob to disguise himself as Esau and receives the blessing of the firstborn - a holy oath that cannot be revoked once spoken. Upon Esau's return with the favored meal Esau learns that the Blessing of the Firstborn has been given to Jacob and he begs his father to bless him also. Rebecca fearing for Jacobs’s safety urges him to leave and go to her ancestral home. Then Isaac dies.

Now some biblical scholars say that Isaac knew it was Jacob disguised as Esau and blessed him accordingly anyway, which begs more questions... but generally speaking that's the long and short of Isaac.

Unless you want to get into the spirituality of the binding of Isaac...