Q: How can one believe in story of J.Smith including his interaction with God and still perfectly believe in the story of Jesus Christ?  
 
A: The same way the one can believe in the New and Old Testament. The Old testament never says that Christ will have to come and restore the Old Testament Church and set his Authority on the Earth again. The Holy Bible is a non stop cycle of restoration and apostasy,  
 
Since the Time of Adam there has been Gospel Dispensations, Noah, Abraham, Moses were each restoring the Priesthood lost to mankind through apostasy from the Gospel.  
 
Eventually Christ himself came to restore truth and reestablish the Church himself, calling Twelve Apostles to lead his Church. Those Twelve though were killed off, plunging the world again into darkness. Until the Dispensation opened through the Prophet Joseph Smith restored the Church to the Earth again.  
 
 
 
1. The bible says that Jesus was sent here and he died for our sins and only through him can we get redeemed. All part of a divine plan. Did this change? 
 
A. Not at all, Christ paid the price for our sins, man's turning away from the Gospel does not remove or nullify the Savior's ministry on Earth. Just like the inability for Israel to follow the Commandments give to Abraham and Moses does not prevent them from receiving those blessings when they did follow the commandments.  
 
The Great Apostasy does not remove the Atonement, all it meant is that mankind was without Apostles and Prophets to guide the people and man made doctrine replaced the divine guidance of the Lord.  
 
2. Joseph smith was told that none of the other churches were true and to start his own or a new church. Where does that leave the other churches that Christ followers started? 
 
A: Correction, Joseph Smith was called to RESTORE the Church Christ put in place. The Prophet was not simply creating a new denomination he was returning to the Earth the only Church that Christ commissioned. One lead by Prophets and Apostles like Paul told us the true Church would be lead by in Ephesians chapter 2.  
 
As for the other Church's that did exist then and have been created since, it has no impact on them since they do not accept the truth of the Restoration. Now that does not mean that Restoration isn't true, and those Churches still have many truths in them, they do not have a fullness of the Gospel though since they are not lead by the revelations of a Prophet like Christ Church is to be lead.  
 
3. Did God the father lose faith in the church that he helped his beloved son start? 
 
 
A: The Church was set up by Christ under the command of the Father according to the Plan of Salvation. Heavenly Father has never lost faith in us, unfortunately mankind did lose faith in him and his chosen leaders the Apostles. They rejected and killed God's leadership and placed uninspired men in there place that were not called of Heavenly Father and did not carry the Priesthood Authority to lead Christ's Church.  
 
4. Isn't it contradictory for Mormons to say that they are Christians when they also believe that christian churches are wrong or not fully right? 
 
Q: Absolutely not, I have yet to see a definition of Christian ever mention following the doctrine of a certain denomination. A Christian is simply one who is a disciple of Jesus Christ, the Son of the Living God and aspires to follow his teachings and example. Catholic, Protestant, or Mormon all follow the teachings of Jesus Christ and declare he is the Son of God so they are all Christians. 
 
There is no contradiction in LDS saying they are Christians, the only contradiction is those who claim to be Christian and persecute the LDS Church since this is against the teachings of Christ.  
 
5. If Joseph smith was a prophet that started a new christian church. Doesn’t that just put him at same level as Jesus Christ if not more? 
 
A: Absolutely not, Joseph Smith is a man, flawed and imperfect like the rest of use. Like Adam, Moses, Elijah, etc he is a Prophet called to preach repentance to the world. All these men though are not close to Christ, he is the Only Begotten Son of God, he is perfect and while he also filled the role of Prophet in restoring the Church he established with Adam once more and preaching to the people to repent, Christ was much, much more than a Prophet. He is the savior the only person who could atone for our sins. No other person could ever do this and no prophet before or after Christ and claim to be equal to Christ.  
 
6. Where exactly did the authority from Jesus Christ get lost? 
 
A: As Paul and Peter taught there had to be a falling away from the truth before Christ would return. This falling away or as LDS call it Great Apostasy, where the Apostles were all killed off or died, was when the authority was lost to the ancient Church. Without Apostles there is no one on the Earth with the Priesthood keys to receive revelation for the Church. Without this revelation there is no way to maintain the purity of the doctrine and prevent doctrine from slowly changing to the desires of men instead of the desires of God.  
 
The Old and New Testaments show how Apostasy has happened throughout time. Ephesians chapters 2 and 4 specifically and repeatedly talk about the need of Apostles and Prophets to lead the Church of Christ. That without them the Church will be tossed by every wind of doctrine like a ship is tossed on the sea during the storm.  
 
The Epistles of Paul alone are evidence enough, each Epistle is filled with doctrinal corrections and rebukes to stop trying to change the purity of the Gospel to the various congregations of the Ancient Church 
 
Study the scriptures deeply and ponder the message with true intent and you can see this clearly even though the Gospel is not 100% complete.

To answer one of your questions, from what I've read Joseph Smith didn't teach that all other churches were wrong he said that they didn't teach the fullness of the gospel of Jesus Christ meaning that there parts to Christ's teachings that they left out or did not know of yet.