Your points are as follows:
1. If free will exists, there is willful act that can ultimately originate within us.
2. If we are not eternal beings, there is nothing can ultimately originate within us.
3. Determinism is true.
4. The idea that we have free will is an irrational idea.
For 2, it equals if there is something that can ultimately originate within us, we are eternal beings. And what you want to argue is that:
1. If there is something that can ultimately originate within us, we are eternal beings.
2. We are not eternal beings.
3. There is nothing that can ultimately originate with us.
If what you are saying is that free will entails eternality, it seems that you presuppose determinism when you think this way since you are assigning an outcome as the property that we can’t have to rule out the existence of free will. For 3, it’s not necessarily true since free will can be compatible with determinism. An easy way to question determinism is that when someone punches your face, you should not blame him because he is not the ultimate source of his actions or he does not have the ability to do otherwise. Free will, the ability to do otherwise, is necessary for moral responsibility.
There are only two options that are, ultimately, source of decisions we execute.
It is either God's decision, or it is God-induced randomness. — Henri
Follow your line of determinism, the ultimate source is God. God determines all we did, do, and will do or God allow randomness of human actions. Given the first, one can say the world with free will agent is better than a world with all human machines controlled by God. If God only creates the world in line of determinism, one can create a world better than God by allowing free will. Therefore, in other for God to be omnipotent, he should have created a world with free will agent.
In conclusion, determinism is not necessarily true when there is alternative like compatibilism which allows free will and hence moral responsibility. If determinism is true, one can create a better world with creatures who can act with free will. Hence, the idea that we have free will is not that irrational as you think it is.