First, I don’t have to demonstrate the truth of something to demonstrate its coherence. You seem to understand my statement perfectly fine, as shown by your follow up questions about it. I’m not seeing any problems with coherence here.
Second, as for demonstrating it: did you choose to post what you did just now? Was that choice not in your control? To put it very briefly, I know that free will exists through first-person experience of it. Feel free to believe that it is an illusion, but I see no reason to do so.
Nope. There’s simply R, S, and the agent who weighs R and S and makes a choice. Not sure why you think there’s something difficult about that. You’ve had to choose between different options before, I assume. The “how” is simply in the agent’s nature (having the capacity to act on reasons) and in the intentionality of the reasons themselves.
You seem to be assuming that the agent’s choice has to be reducible to or entirely explicable by psychological or neurophysiological facts - that the “how” can be further broken down in those terms - but that is not an assumption I would grant. Again, feel free to disagree; my point is that it appears entirely coherent.