I call that denying the divinity of Jesus. Arius taught that Jesus was a creature specially created to create the rest of creation (if I recall, taken from Plato’s thoughts on the demiurge). He was the ‘son of God’ by adoption not by right or nature and he was of like substance (homoiousios) or different substance (heteroousios) (they changed terminology from time to time). Jesus was also given god-like powers – particularly in helping to create the rest of creation.To be not of the same substance (homoousios) as the Father is to my mind (and the minds of the Church Fathers, such as Saint Athanasius), is a direct denial of Jesus’ full divinity.
Homoiousios was proposed by Eusebius and others to reach a compromise between
heteroousios (the Arians) and
homoousios (the orthodox). Arians believed Jesus was divine, but not to the level Christians did. Islam, on the other hand, denounces that Christ had anything to do with the essence of God.
Again, most acknowledge modern day Arians to be Jehovah’s Witnesses.
Yes, that is the denial of the Hypostatic Union (and all its variations). But, whereas Arianism tended to emphasis the human side of Jesus (to denying the divinity of Jesus), Nestorianism emphasized the divine side of Jesus (to the denying of the humanity of Jesus – in some variations of the heresy).
I wouldn’t say they emphasized the divine aspect, since they believed the divine side of Jesus didn’t even belong to Jesus. Nestorius, in his letter sent to the council, even argued that Jesus told His disciples “Destroy this temple and in three days I will raise it up” and not “Destroy my godhead and in three days it will be raised up.”
Again, they called Him the Christ (hence the Virgin Mary was the
Christotokos), but not a divine being (or she would be the
Theotokos). The anathema given at the Third Ecumenical council was “if anyone does not confess that Emmanuel is God in truth, and therefore that the holy virgin is the mother of God (for she bore in a fleshly way the Word of God become flesh).”
I’ve never heard a Muslim claim that the Koran was God.
You don’t understand how Muslims define “the Word.”

To quote Saint John Damascene:
And again we say to them: ‘As long as you say that Christ is the Word of God and Spirit, why do you accuse us of being Hetaeriasts? For the word, and the spirit, is inseparable from that in which it naturally has existence. Therefore, if the Word of God is in God, then it is obvious that He is God. If, however, He is outside of God, then, according to you, God is without word and without spirit. Consequently, by avoiding the introduction of an associate with God you have mutilated Him. It would be far better for you to say that He has an associate than to mutilate Him, as if you were dealing with a stone or a piece of wood or some other inanimate object. Thus, you speak untruly when you call us Hetaeriasts; we retort by calling you Mutilators of God.’