Not quite. I referred to the Jesus Christ whose life and work are described in the gospels, not somebody else who may carry the same name. As for doctrine, I would not be so foolish as to accept any doctrine "no matter what" without first hearing it. No doubt some doctrines are incompatible with the teachings of Jesus Christ.
That said, I believe that faith, hope, and charity are far more important than doctrine. In other words, one can hold to an erroneous theology and still be a good Christian.
To be a Christian is to have a personal commitment to follow Jesus Christ. If a person professes such a commitment and calls himself a Christian, I am disinclined to say otherwise merely because I may disagree with him on some point of doctrine.
To answer your other questions, I would cite the prophecy of King Benjamin (ca 124 B.C.) in the Book of Mormon as an excellent summary of who Jesus Christ is and what He has done for us:
5 For behold, the time cometh, and is not far distant, that with power, the Lord Omnipotent who reigneth, who was, and is from all eternity to all eternity, shall come down from heaven among the children of men, and shall dwell in a tabernacle of clay, and shall go forth amongst men, working mighty miracles, such as healing the sick, raising the dead, causing the lame to walk, the blind to receive their sight, and the deaf to hear, and curing all manner of diseases.6 And he shall cast out devils, or the evil spirits which dwell in the hearts of the children of men.
7 And lo, he shall suffer temptations, and pain of body, hunger, thirst, and fatigue, even more than man can suffer, except it be unto death; for behold, blood cometh from every pore, so great shall be his anguish for the wickedness and the abominations of his people.
8 And he shall be called Jesus Christ, the Son of God, the Father of heaven and earth, the Creator of all things from the beginning; and his mother shall be called Mary.
9 And lo, he cometh unto his own, that salvation might come unto the children of men even through faith on his name; and even after all this they shall consider him a man, and say that he hath a devil, and shall scourge him, and shall crucify him.
10 And he shall rise the third day from the dead; and behold, he standeth to judge the world; and behold, all these things are done that a righteous judgment might come upon the children of men.
11 For behold, and also his blood atoneth for the sins of those who have fallen by the transgression of Adam, who have died not knowing the will of God concerning them, or who have ignorantly sinned.
12 But wo, wo unto him who knoweth that he rebelleth against God! For salvation cometh to none such except it be through repentance and faith on the Lord Jesus Christ. (Mosiah 3:5-12)
When will you have the assurance that you have eternal life in Christ, as an absolute certainty?
And I would point out to you the prophecy of Gandalf the Grey from the Book of the Hobbit: "All we have to decide is what to do with the time that is given to us. There are other forces at work in this world Frodo, besides the will of evil.”
A much more readable work of fiction BTW than the Book of Mormon.