Free Will exists. Your arguments prove that it does. Knowing and understanding the same requires to know a little more about the soul or life atom that makes a body alive.

The brain is just the hardware. The understanding and the decision making and feelings all happen in the life atom.

There is coexistence of the physical body and the life atom in the form of a human being a homo sapien. Being sentient the right and wrong aspect is hard-coded and instilled into the life atom. The various faculty in the life atom have the ability to connect to the transactive memory cloud of the society in which the child grows up.

The faculty in the soul validates the learning from the society. Academic education is a very small subset of the whole learning process. After a certain age the human being wants to live by what he has learnt from the society. During that living period validation of his learning with the hard wired moral right and wrong happens.

Invariably every human being then finds gaps and voids and wants to fill them and improve his learning. That is the story with all of us. We all have this stage in life. Some have it early some pretty late.

At the end of the journey when they know that the coexistence is going to end and the soul or life atom is going to detach from the body there are regrets for wrong doings. These mistakes or morally wrong doings have been a result of the wrong learnings from society. The rest of the life the human being tries to teach young ones the correct morally right things.

We as a race need to create a society where a child can grow and learn to use the free will to learn and do only morally good things.

That is coexistence philosophy on which you will find some content on my blogs.