Is the book Isaiah in Jewish holy scripture?

Answer 1

Yes, it is. Here are the contents of the Tanakh:
The Jewish holy book is the Tanakh (Jewish Bible), containing the Torah and the prophetic books.
Tanakh is a Hebrew acronym of T, N, K which stands for the three parts of the Tanakh: Torah, Nevi'im (Prophets), and Ketuvim (Writings).

1) The Torah (תורה), also called the Pentateuch, is the primary Jewish holy book. It is comprised of the 5 Books of Moses (also called the Books of the Law). The Torah was given by God to Moses (Exodus 24:12), who transmitted it to the people and wrote it (Deuteronomy 31:24).

1-5: The Torah, or Five Books of Moses:
• Bereshit (Genesis)
• Shemot (Exodus)
• VaYikra (Leviticus)
• BaMidbar (Numbers)
• Devarim (Deuteronomy)

2) Nevi'im (נביאים), The Prophets. The Jews see the book of Prophets as the Divinely-inspired story of their past and the relationship between God and Israel. Jewish tradition (Talmud, Bava Batra 14b) states that the prophetic books were written by the authors whose names they bear: Joshua, Samuel, Isaiah, Jeremiah, Ezekiel, Hosea, Joel, Amos, etc. Judges is credited to Samuel, Kings was written by Jeremiah. The Prophets is comprised of a total of 8 books according to the Jewish count.

6-9: The Nevi'im Rishonim, the Early Prophets:
• Yehoshua (Joshua)
• Shoftim (Judges)
• Shmuel (Samuel I and II)
• Melachim (Kings I and II)

10-13: The Nevi'im Acharonim, the Later Prophets:
• Yeshayahu (Isaiah)
• Yirmiyahu (Jeremiah)
• Yechezkel (Ezekiel)
• Trei Asar ("The Twelve Prophets" or Minor Prophets)
Books and Prophets within Trei Asar:
• Hoshea (Hosea)
• Yoel (Joel)
• Amos
• Ovadiah (Obadiah)
• Yonah (Jonah)
• Michah (Micah)
• Nahum
• Havakkuk (Habakkuk)
• Zephaniah
• Haggai
• Zechariah
• Malachi
3) Ketuvim (כתובים), Writings. The Ketuvim contains the remaining History Books: Daniel, Lamentations, and others. Jewish tradition (Talmud, Bava Batra 14b) states that the prophetic books were written by the authors whose names they bear: Daniel, Ezra, Nehemiah, etc. Ruth was written by Samuel; Lamentations was written by Jeremiah; Psalms was set in writing by King David; Chronicles was written by Ezra; Proverbs, Song of Songs and Kohellet (Ecclesiastes) were written by King Solomon; and Esther was written by Mordecai and Esther. Concerning Job, the Talmud states more than one opinion as to when it was written. The Writings consists of 11 books by the Jewish count:

14-16: The "Sifrei Emet"
• Tehilim (Psalms)
• Mishlei (Proverbs)
• Iyov (Job)

17-21: The "Five Megilot" (Five Scrolls)
• Shir HaShirim (Song of Songs)
• Ruth
• Eichah (Lamentations)
• Kohelet (Ecclesiastes)
• Esther

22-24: The rest of the Writings:
• Daniel
• Ezra-Nehemiah
• Divrei HaYamim (Chronicles I and II)

Further information:
The term Torah can refer loosely to the entire Jewish Bible.

Tradition places the sealing of the Tanakh around 340 BCE.

Answer 2

Yes. The Book of Job makes up part of the section of the Tanakh (Jewish Bible) called the Writings.

Answer 3

Yes, Isaiah is included in the Tanakh.