I have tried to have a consistent approach to forgiveness to include both the OT and NT teaching.You are trying to lump all sorts of different things into one and it doesn't work that way.
Regarding the covenant with Israel it was a bilateral covenant, and a land covenant,meaning God says you can keep this land and I will bless and protect you IF; and then He sets the conditions they have to meet. The passage that says if you humble yourselves and pray etc. Says nothing about repentance.
The sacrifices were a temporary covering (pointing to Jesus)for sin so God didn't have to destroy them. Nothing about repentance, you injected that into the passage.
Did Cain repent?
The tax collector wasn't repenting he was recognizing that he was a sinner and only God's mercy could preserve him.
I realize the Bible says in places, repent and be saved but it also says be baptized and be saved, yet most Christians understand that neither repentance or baptism saves anyone, only Faith in Jesus does. Baptism is a representation of our dying and being raised with Christ, and repentance shows we have recognized our sin against God and desire to no longer do those things. I don't believe we can truly repent until we are saved. We can be sorry. We can know one things are wrong and make human effort to fix ourselves. But repentance in the Bible has to first recognize our offense AGAINST GOD. Not people. Until we are saved, in Christ, we will never recognize this
What you ignore is what Jesus taught in Luke 17, where forgiveness is only on repentance. This together with the consistent OT teaching of the need for repentance changes how you view forgiveness.