Are Judaism Christianity and Islam are monotheistic?

Answer 1

Because of the belief and tradition founded by Abraham. According to Jewish tradition, Abraham (18th century BCE) came from ancestry that had been God-fearing a couple of centuries earlier but had afterwards slipped into idolatry (Joshua 24:2). Nimrod, the idolatrous tyrant, had brought Abraham's father (Terah) from the Semitic ancestral seat near the conjunction of the Balikh and the Euphrates, and instated him in a position of power in his army in the royal Babylonian city of Ur, where Abraham was born. Nimrod persecuted any who would question his idolatrous cult.

The Kuzari (Rabbi Judah HaLevi, 1075-1141) states that Abraham was gifted with high intelligence; and, as Maimonides (1135-1204) describes, Abraham didn't blindly accept the ubiquitous idolatry. The whole populace had been duped, but the young Abraham contemplated the matter relentlessly, finally arriving at the conclusion that there is One God and that this should be taught to others as well. This is what is meant by his "calling out in the name of the Lord" (Genesis ch.12). As a young man, he remonstrated with passersby in public, demonstrating to them the falsehood of their idols; and our tradition tells how he was threatened and endangered by Nimrod.

Subsequently, Terah relocated to Harran; and it is here that Abraham began to develop a circle of disciples (Rashi commentary, on Genesis 12:5).

Later, God told Abraham in prophecy to move to the Holy Land, which is where Abraham raised his family.

He continued his contemplations, eventually arriving at the attitudes and forms of behavior which God later incorporated into the Torah given to Moses.

Abraham, with God's help, singlehandedly trounced the supremacy of the evil Nimrod. He received God's promise of inheriting the Holy Land (Genesis 13). He strove to raise a family (Genesis ch.15, 17, and 24) which would serve God (Genesis 18:19); and God eventually blessed his efforts, granting him many children (ibid., ch.16, 21 and 25), as He had promised (Genesis ch.17). Abraham was the ancestor of the Jewish people and lived to see his work live on in the persons of Isaac and Jacob; and he taught many other disciples as well (Talmud, Yoma 28b). He saved the population of the south of Canaan from invading foreign kings (Genesis 14); and he was feared by neighboring kings (ibid., ch.12 and 20). Abraham gave tithes (Genesis ch.14), entered into a covenant with God (Genesis ch.15 and 17), welcomed guests into his home (Genesis ch.18) unlike the inhospitable Sodomites (Genesis ch.19), prayed for people (Genesis ch.18), rebuked others when necessary (Genesis ch.20), eulogized and buried the deceased (Genesis ch.23), and fulfilled God's will unquestioningly (Genesis ch.22). He became renowned as a prince of God (Genesis 23:6).

All of these forms of behavior were based upon the ways of God, which Abraham comprehended through his contemplations. These, and similar personality traits, were the teachings of Abraham and his descendants (unlike idolatry, which had tended to go hand in hand with cruel, licentious and excessive behavior, since the caprices which were narrated concerning the idols were adopted as an excuse to imitate those types of behavior).

It is therefore clear why God expresses His love for Abraham (Isaiah 41:8) and calls Himself the God of Abraham (Genesis 26:24), and says that Abraham obeyed Him fully (Genesis 26:5).

Answer 2

Yes.

Answer 3

Yes.