Why did Jesus or anyone have to die for our sins? 

Without the shedding of blood there is no forgiveness (Heb 9:22).

What was the price that was paid for my sin?

Forasmuch as ye know that ye were not redeemed with corruptible things, as silver and gold…But with the precious blood of Christ, as of a lamb without blemish and without spot (1 Peter 1:18-19).

 Is Jesus the only one who can save us from our sins?

 Jesus said to him, “I am the way, the truth, and the life.  No one comes to the Father except through Me” (John 14:6).  

Nor is there salvation in any other, for there is no other name under heaven given among men by which we must be saved (Acts 4:12).

In him [Jesus] we have redemption through his blood, the forgiveness of sins, in accordance with the riches of God’s grace (Eph 1:7).