They are not. The Talmud is commentary on the Hebrew Bible. See also:
http://judaism.answers.com/jewish-literature/the-writings-of-judaism-torah-talmud-and-more
They are two distinct things but are intertwined. The Hebrew Bible is prophecy, while the Talmud is oral tradition which serves to explain the Hebrew Bible and its laws, and to add non-prophetic further information such as subsequent history, lives of the Sages, allegories, etc.
The Tanach (Hebrew Bible) is not in the Talmud. The Talmud contains commentary on the Tanach.
The Psalms are in the Tanakh (Hebrew Bible), not in the Talmud.
The Torah, the rest of the Hebrew Bible, and the Talmud (Oral Law). See also the Related Links.Link: More about the TorahLink: The Hebrew BibleLink: More about the Talmud
For Jews, the next in importance is the Talmud.
The Hebrew Bible (Tanakh) and the Talmud.
It probably comes from the fact that the Hebrew Bible is very accessible to most Christians and is used often to set the scene for Jesus' life. The Talmud came later and while it is important, its importance comes from the fact that it interprets the Hebrew Bible, not on its "own merit". The Hebrew Bible is the Holy Book, not the Talmud. It is similar to how the Nicene Creed is central in Christianity, but few Americans are aware of the Nicene Creed, even though they are aware of the Christian Bible.
The Tanakh (Hebrew Bible) and the Talmud would both be correct answers.
The teachings of Judaism can be found in the The Hebrew Bible, the Mishna, The Talmud, and many other texts.
They are records of occurences among the Hebrews. They are included in the Hebrew Bible, the Talmud and midrashim, and other ancient works.
The Book of Kings was written by Jeremiah, who also wrote Lamentations as well as the Book of Jeremiah (Talmud, Bava Bathra 14b). See also the links.Link: History of the Hebrew BibleLink: Reliability of the Hebrew Bible
The word לילת occurs in the Hebrew Bible as a noun meaning "night spirit" but it does not occur as a Name. The character of Lilith (Adam's first wife) is only mentioned in the Talmud.
The Tanakh (Hebrew Bible) and the Talmud are the most authoritative. Pretty much everything else is derived from these two.