Was Abraham the first hebrew?

answer: absolutely. To correct another - Abram's father was a pagan, a creator of idol statues. HaShem called Abram to leave his pagan ways and follow Him and only Him.

In addition, Judaism passes through the mother, not the father. So, even if his father had been a Hebrew/Jew, it wouldn't have passed to his son. Tribal lineage was through the father and that didn't exist at the time since Abram (who became Abraham) was the first Hebrew/Jew and tribe came later.

Not exactly.

Many historians believe that Abraham was a metaphor for a tribe/group of people who migrated from Mesopotamia to Canaan/the land of Israel in antiquity. These people might have contributed to the formation of the Israelite/Jewish ethnicity. In fact, genetic studies show many modern Jews, especially those from Europe, North Africa, and the Middle East, share DNA with Kurds, who live in the area where the biblical Abraham probably came from.

So Abraham was a Mesopotamian, perhaps proto-Amorite or Sumerian or some sort of Semite, but not a hebrew/Israelite.

Jacob is the patriarch of the Jews and grandson of Abraham so I would say that Abraham was the first Hebrew.

It looks that way to me. Here is the first use of the word "Hebrew" in Scripture.

Gen 14:13 Then one who had escaped came and told Abram the Hebrew....

He was Hebrew. Abraham was not first born. But known as his father's first sons due to his outstanding faithfulness towards God.

He was the first person called Hebrew. But obviously his father must've been a Hebrew before him.

No. Most likely Eber was.