Answer 1
There is no mention of Muhammad in the Torah, Neviim or Ketuvim. He was born long after they were written. Judaism considers him as a regular person, not a prophet.
Answer 2
Mohammed has no role in Judaism and he is considered nothing more than a human who led Arab tribes; no different than any other Arab Sheikh. The issue with Mohammed's "prophecy", from a Jewish perspective, comes from five objections to what he claimed and preached, as well as The Bible's inability to support him:
- Prophecy Post-Malachi: Judaism believes that each generation has a weaker connection to God than the previous generation. Judaism also holds that a person has to have a naturally strong connection to God in order to prophesy. Therefore, around the time of the Prophet Malachi, humanity was losing the strength to maintain prophesy. Jews therefore claim that since Malachi, no person is capable of prophesying successfully. As Mohammed lived over 900 years after Malachi died, Mohammed therefore could not be a Prophet.
- Disagreements with the Torah: Mohammed claimed that he received Divine Revelations that explicitly contradicted the Torah such as the claim the Ishmael was taken to be sacrificed instead of Isaac. Mohammed claimed that any differences between what his revelations and the Torah was due to corruption from bad Jews. This infuriated Jews who maintained that their scripture was the same one that they had been using for centuries. He was disagreeing with the words of the Torah and according to Deuteronomy 13:1-4, anyone who openly disagrees with the words of the Torah is a false prophet at best.
- Inclusion of Christian Tradition: Mohammed said that Jesus and John the Baptist were prophets when the Jews did not believe so. Jesus was seen in the Jewish community as not only a heretic, but the cause of much Jewish suffering because of Christian persecution. Jews could not accept the religious leadership of someone that supported Jesus as a legitimate prophet. Of course, Jews also rejected Jesus for substantial religious reasons which Mohammed did not take the time to hear out. Muslims today often do not know what the Jewish perspective was on Jesus that led to their rejection of him. (A related question addresses that particular issue: Why Jews rejected Jesus?)
- Different Rules: Islamic Law was not the same as Jewish Law. While there were certainly similarities, it was a different law and Jews were not going to give up their traditions and history to join a new religious group. To many Jews, it was another example of all of the previous religions that had tried to convert them away from their proper mission.
- No Biblical Prophecy for Mohammed: Muslims often incorrectly point to Song of Songs 5:16 which has the Hebrew word "Machmadim" in it to place Mohammed in the Bible. This fails to realize that (a) "Machmadim" is an actual Hebrew word meaning "lovely" or "nice" and (b) that Song of Songs Chapter 5 is detailing a love story, not a prophecy. There is nothing else in the Bible that can even be bent out of shape to support the arrival of Mohammed.
The Section of the Bible is provided below with the word Machmadim in bold. As is clear, this is a love song, not a precursor or prophecy.
Song of Songs 5:10-12, 16: (NIV): My beloved is radiant and ruddy, outstanding among ten thousand. 11 His head is purest gold; his hair is wavy and black as a raven. 12 His eyes are like doves by the water streams, washed in milk, mounted like jewels....16 His mouth is sweetness itself; he is altogether lovely. This is my beloved, this is my friend, daughters of Jerusalem.