No. Joseph (son of Jacob) was an Israelite, born to two Hebrew parents in Canaan. He later lived for several decades in Egypt. See also:
Tzophenath Paneach
Joseph
Joseph was named as Zaphenath-paneah by Pharaoh as per Genesis 41:45. This name was given to Joseph when he was promoted as Prime Minister.
His brothers were jealous and so they sold him into slavery
Initially, no. They believed that he was just another Egyptian Minister.
Joshua was an Israelite, descended from Ephraim son of Joseph.
It was Poitphar the captain of Pharoah's guard. Genesis 39:1 Now Joseph had been taken down to Egypt. And Potiphar, an officer of Pharaoh, captain of the guard, an Egyptian, bought him from the Ishmaelites who had taken him down there.
Franz Joseph Lauth has written: 'Aegyptische Chronologie' -- subject(s): Chronology, Egyptian, Egyptian Chronology 'Moses-'Hosarsyphos-Sali-Hus Levites-A'haron frater Ziphorah-Debariah' -- subject(s): Accessible book
Yes, he is shown in the Egyptian written documents
Joseph Gilbert Manning has written: 'The Hauswaldt papyri' -- subject(s): Demotic Papyri, Egyptian language, History, Papyri, Demotic, Sources
The name Joseph is Hebrew. The Pharaoh did not give Joseph a Hebrew name, he gave him an Egyptian name, which was Zaphnathpaaneah. Genesis 41:45 And Pharaoh called Joseph's name Zaphnathpaaneah; and he gave him to wife Asenath the daughter of Potipherah priest of On. And Joseph went out over all the land of Egypt.
Joseph's brothers did not recognize him because he was dressed as an Egyptian ruler, which he was. Also, it would have been the last place where they would have expected to find the brother they had sold into slavery.