Why is Jesus' sinlessness important to understanding your salvation?
Jesus's sinlessness is critical in that God's law required that blood be spilt over the atonement for sin. If Christ had any sin, He would have to pay with his own blood. But (praise be to God) Christ was sinless paving the way for those to accepting His gift to be saved.
In what way do you think Jesus suffered when your sins were poured into his soul?
I think Christ's greatest suffereing came when God, the Father, had to "look away". This separation came at the cross, when Jesus exclaimed: in Matt 27:46 "Eli, Eli, lama sabachthani?" that is, "My God, My God, why have You forsaken Me?"
How could a sinless Man stand this kind of corruption?
Part of how Christ could have stood such corruption was because Jesus was obedient to the Father. In that obedience, Jesus could stand against the sinful corruption of those that brought this violence upon Him.