English Wikipedia is generally not a good source for in-depth, accurate understanding of Jewish topics. Often, the overlap between those who get it right and those who enthusiastically edit Wikipedia is small. In this case, you are interpreting the word choice of a secondary source, that is, what some random Wikipedia editor understood of the underlying primary source in Bava Batra 15b, especially in your question about "most rabbis". The account in Wikipedia is somewhat botched, even before your attempt to interpret it (e.g. in omitting the "exception" even according to the standard version of the text).
The five rabbis in that primary source, a brayta (Tannaitic unit of teaching) on Bava Batra 15b, don't explicitly speak of whether Iyov was Jewish or gentile, or whether he was a prophet. Rather, they each weigh in with a position of when Iyov lived. The Talmud, or to be more specific, the anonymous narrative voice of the Talmud (called the setama degemara), a stratum composed many centuries later, makes this deduction that "these tannaim necessarily considered Job an Israelite", with the exception of the one Tanna who placed Iyov fairly early.
The basis of this deduction is logical, and rests on two premises, namely that after a certain time, Divine inspiration or prophecy would not rest on a gentile, and secondly, that Iyov was such a person who was privy to such prophecy, presumably based on verses such as Job 40:1, "Moreover the LORD answered Job, and said..."
Meanwhile, the Wikipedia statement regarding the Talmudic text of "R. Chananel ben Chushiel" is a reference to Rabbenu Chananel. He version is cited in a comment by the Tosafists on the page:
בפירוש רבינו חננאל גרס כולהו תנאי ואמוראי מודו דאיוב ישראל היה ולר"י נראה דל"ג ואמוראי דרבא ע"כ סבר לעיל דלאו מישראל הוה דקאמר לעיל הכי אמר להן משה למרגלים ישנו לאותו אדם ששנותיו כעץ כו':
where he includes not just Tannaim (those in the brayta) but also Amoraim (later generations of scholars), as also maintained that Iyov was Jewish. Tosafot cites the R"i who says that this is an incorrect version, because one of the Amoraim earlier in the gemara in question, Rava, considered Iyov a gentile.
However, in terms of your question,
"Was he considered an Israelite, or a Gentile, according to the opinion of most rabbis?"
you might be reading too much into the wording of the Wikipedia editor. When explaining the meaning of "all the Tannaim", Rashi there explains it as:
וכולהו הני תנאי כו' - מסקנא דתירוצא הוא דתריץ לעיל תנאי היא ההוא מתניתא דלעיל ס"ל עובד כוכבים הוה והני תנאי דהך מתניתא כולהו סבירא להו דישראל הוה בר מיש אומרים דאמרי בימי יעקב הוה:
That is, this is a Tannaitic dispute, that one Tannaitic source above maintains that he was a gentile, while these Tannaim of this particular brayta maintain that he was a Jew.
For reference, there were approximately 3000 rabbis among the Tannaim and Amoraim. Here, we are counting independently listed opinions, which could be counted on two hands. That does not tell us what "most rabbis" of these 3000 held, about him being Jewish or gentile.
It also does not tell us explicitly as to whether they deemed him merely righteous man or a prophet, in terms of your first question. (A better practice in asking questions here is separating multiple questions into separate posts, since each can get complicated, and people might be able to answer one but not the other.) Rather, this is the assumption of the anonymous voice of the Talmud, that is assuming that all these Tannaim accepted that Iyov received some Divine message, again presumably based on the verse, and then extrapolating on that basis.
However, this is not necessarily the case. For instance, we see that according to Rabbi Shimon ben Lakish, despite Iyov existing as a real person in the days of Abraham (and by extension, probably also not being Jewish), the account in the Book of Iyov of his sufferings and the ensuing conversations (which would presumably include the divine revelation) did not actually occur. Rather, it is Wisdom Literature, exploring the problem of why bad things happen to good people, and this fictional setup was ascribed to this real historical person because he was a such a good person that he would have withstood the tests and tribulations.