Hello/Salaam
First, asking God for forgiveness is recommended but we can never be sure if He will forgive us. That is because we cannot command His Will, nor can we know what God will do. We know that His Mercy is great and for this reason, people continue to believe that He forgives sins.
Second, only believing and sinning through behaviors and breaking the laws truly do not go together. Your actions trully portray your beliefs. God knows that and if one trully repents and asks for forgiveness, stopping to commit sin behaviorally/morally/spiritually/etc. then it is more likely that the person will be forgiven.
Third, one does not need to shed blood to earn forgiveness. God in the Holy Qur'an states that a Muslim must not sacrifice anything in anyone else's name, but Only in God's name. The sacrifice in Islam is in remembrance to the son Prophet Abraham savs was about to sacrifice and Prophet Abraham savs, as a reminder to the believers of his great faith in God.
We believe Jesus savs to be Messiah and to be one of the greatest Prophets, but we do not believe him to be god/divine. He was only a human being.
While Revelations (Bible and Qur'an) are from One, True God, He prescribed laws for all of the followers of these Holy Books, but for some he made certain laws that others do not have to follow. For instance, Muslims are commanded to pray five times a day. Jews pray less than that. Muslims do not have to sacrifice to purify themselves constantly from sins. Rather our purification comes from constant praying. Jews were prescribed sacrifices.
Christians seem to have it the easiest for some reason. But that does not mean that these commands come from other than Our Lord. After all, He has a Master Plan for everything, no?