>Choice is the ability to consciously determine a course of action for ourself from a set of alternatives.
>So the alternatives we assess and end up rejecting were never truly available to us.
Therefore, choice is nothing more than an illusion.
>Nevertheless, we chose what we did choose.
Not really. If the alternatives were never truly available in the first place, how can you say that you made a choice? An analogy would be imagining yourself on a railroad car. There's a fork in the tracks, but the switcher has been shifted so that the railroad car will only be able to go down one path once it reaches the fork, and nothing can make it go down the other path. There is the appearance of there being multiple possible outcomes, but really, there's only one path the railroad car can take.
>Impossible for what to affect the outcome of events? Anything? Even the entities involved in the event itself?
Yes, anything.
I'll try to make an analogy for this as well. Imagine the big bang setting forth into motion all the particles and energy in the universe. Now imagine the particles are billiard balls, and the universe is a pool table. Nothing can affect the motion of the balls without some sort of intervention from outside the table(universe.) Because the balls have already been set in motion and nothing can alter them, it's not really accurate to say that one ball is altering the path of another if they happen to collide. That collision could have been predicted from the moment the balls began their motion, so really they're just proceding along their natural course.
Now to throw quantum physics into the analogy (in a very rudimentary way.) Imagine that one of the balls has a 75% chance of being in location A on the table, and a 25% chance of being in location B on the table. It's impossible to predict with absolute certainty whether the ball will ultimately manifest itself at location A or B (only that it's more likely that it will manifest at location A,) so there are two possible outcomes of ball motion that can occur. However the balls themselves are still completely unable to change the ultimate location of the quantum ball and the subsequent motion.
That being said, and going back to my initial assertion that free will is just an illusion, humans are ultimately just made up of billiard balls, and nothing can be doneto affect their motion. There may be multiple paths of motion depending on where the quantum balls manifest themselves, but to say that you can choose to affect something is like saying one billiard ball "chose" to strike another.