The issue of trinity; one is three and three is one, the issue of the son of God, raising Jesus to a divine status, God becoming a man or the fully man, fully God thing, a person dies for the sins of other people, all of this is rejected in Islam and opposes firm Islamic principles not to mention that Christians themselves are not able to explain a concept like the trinity.
Islam is clear and simple. God is one, unique and has no opposite and no partners, so He is not two or three or any number whether all of them are manifestations of the same entity or three separate persons but the same God....etc.
God is the Creator and the creator is distinct from the creation. Thus the "son of god" concept is absolutely rejected. Mortals try to extend through their off-springs but if God is eternal and self-sufficient, for what His need to any son would be?
The relationship between God and us is the relationship of a creator and creatures, is the relationship of Ilah (the only One who deserve to be worshiped) and 'Abeed (who worship and submit to Him and belong to Him). As all in the Heavens and Earth belong to Allah, there isn't any place for anyone to be His son.
"O People of the Book! Commit no excesses in your religion: Nor say of Allah aught but the truth. Christ Jesus the son of Mary was (no more than) an apostle of Allah, and His Word, which He bestowed on Mary, and a spirit proceeding from Him: so believe in Allah and His apostles. Say not "Trinity" : desist: it will be better for you: for Allah is one Allah. Glory be to Him: (far exalted is He) above having a son. To Him belong all things in the heavens and on earth. And enough is Allah as a Disposer of affairs." An-Nisa': 171
The other point Islam establishes the values of justice thus personal and individual responsibility and accountability for actions is a fundamental Islamic concept. There is nothing called God tortures a person for sins of other people. Every one is held responsible and accountable for his own actions. Plus, when someone commit a mistake or a sin, all what he/she has to do is to repent which means stopping the sin and ask forgiveness from God and his/her sins will be abolished, not just this but "Unless he repents, believes, and works righteous deeds, for Allah will change the evil of such persons into good, and Allah is Oft-Forgiving, Most Merciful" Al Furqan: 70
If Adam committed a sin, then he is the only one responsible for his sin. In addition, God basically forgave him. So a concept like the "original sin" is refuted according to Islam and would be very unjust.
Jesus wasn't killed or crucified, whether his body and soul were raised to Heaven or his soul only after death, this detail is not clear in the Qur'an:
"That they said (in boast), "We killed Christ Jesus the son of Mary, the Messenger of Allah.;- but they killed him not, nor crucified him, but so it was made to appear to them, and those who differ therein are full of doubts, with no (certain) knowledge, but only conjecture to follow, for of a surety they killed him not" An-Nisa'
"Behold! Allah said: "O Jesus! I will take thee and raise thee to Myself and clear thee (of the falsehoods) of those who blaspheme; I will make those who follow thee superior to those who reject faith, to the Day of Resurrection: Then shall ye all return unto me, and I will judge between you of the matters wherein ye dispute." Ali Imran