As I read the Old Testament, I saw that there was no sacrifice for murder or adultery. Why was this, and how can we be sure that these sins are forgiven under the new covenant?
There was no sacrifice for these crimes because they were punishable by immediate execution. The punishment for murder is given in Numbers 35:16-18 and for adultery see Lev. 20:10. We can be sure that they are forgivable under the New Covenant because all sins are forgivable except the sin of refusing the pardon Jesus purchased for us with His life. (Colossians 2:13-15)