Absolutely. 
 
We believe that Jesus was the only perfect person in the history of the earth. Everyone else has sinned. The only way for us to return and live with our Heavenly Father is to become cleansed from our sins. The only way to repent and become clean is through Jesus. Jesus Christ suffered in Gethsemane and died for us on the cross so that through his atonement we can be saved. 
 
Here's a link with some good overview information on our beliefs about Jesus Christ: 
http://mormon.org/jesus-christ/ 
 
Absolutely.

I have too many weaknesses to list. Jesus came for the sinners, not for those that are whole.

The only one who has never committed sin is Jesus Christ. All others have sinned and fallen short of the glory of God.  
 
If we did not believe this we could not be Christians, for this is a fundamental teaching of the Gospel.

But, dont you believe that a mormons are saved by works and not by grace as believed by non-mormon christians. This would make salvation unattainable by mormons.