You said that god gives each man a soul at the moment of conception.
Yes.
That makes god the causing agent of that soul, not the physical parents.
Yes. The parents being the only causing agents is called traducionism. Of course parents are causing agents too, this process needs sex.
God isn't bound by any law according to which he must abide to give a soul to every fertilized human egg.
He's bound by His nature. He can't lie or be evil, for instance. The nature, the will and the intellect of God/angels/men are very distinct things.
He made a pact with Adam and every descendant of Adam must have a soul.
He has a choice to give it or not give a soul.
Idk.
By causing a soul to exist, god is taking responsability for such soul.
In a sense yes. He must give opportunities to this soul.
If god is the causing agent of the existence of that soul, it is entirely god's responsability that such soul is made to pay for the original sin.
Idk if I understand what you mean.
Because, you know, he chose to create that soul.
He has made a pact.
If, because of the original sin, that human is born defective, or dies in a horrific tsunami, it is entirely god's will.
No.
Because an almighty god could a) decided to not give that human a soul;
Maybe He has no choice.
b) have crated a world where tsunamis didn't exist, because they're entirely not needed for life to exist;
I don't agree. How do you know is possible to exist worlds suitable for free-willed beings in a physical world without natural laws?
c) have created a world where humans would be miraculously protected from natural disasters and genetic defects.
Same thing. How do you know that?
And finally, after injustly subjecting millions of human beings to needless suffering during their physical life, god decides, after a few years, to resign from responsability towards the soul he created by doing nothing to stop that soul from falling into a perpetual state of sentient nihil.
I wonder - is this a god worth believing and worshipping?
I don't agree with your premises so I can't accept your conclusion.