I'm gonna try to answer your post to the best of my ability Lithose, some other people may want to chime in with some points they think they can make better as well.
So first:
You've gotten your definition of entropy wrong. Entropy is energy that has become unavailable for use as work energy, and entropic energy is more disorganized, not more organized. Organized energy is energy capable of doing work.
entropy - Google Search
en?tro?py
'entr?pe/Submit
noun
1.
PHYSICS
a thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.
2.
lack of order or predictability; gradual decline into disorder.
"a marketplace where entropy reigns supreme"
So when you say
.You have a liquid medium (Water) that facilitates entropy (Dissolution of energy through chemical recombination?)
you've got an error in comprehension there (which, having not had chemistry in a decade and then only an intro course, is perfectly reasonable).
So then when you reach this conclusion
Energy (Sunlight) hits this puddle of muck; and since the muck puddle now has a higher state of energy, entropy favors chemicals which will bring the energy lower?
You've kinda gotten it backwards. More energy in the medium -> More organized energy in the system -> More energy able to do work like drive reactions forwards. Living molecules are better at taking this organized energy and utilizing it more efficiently, so they are favored in high energy situations.
Here's the thing, if these reactions release more energy than they take in...why are they favored through the forces of entropy?
In any chemical reaction, only some of the total energy is lost as entropic energy (basically heat), and there are reactions which produce MORE energy than it takes to form their bonds initially. The words you're looking for here are exothermic and endothermic (releases energy and retains energy, respectivley) In fact, one molecule of particular note that does this is Adenosine Triphosphate, or ATP, the key molecule that powers pretty much all living organisms on this planet. ATP is produced through glycolysis, the breaking down of glucose in reciprocation with respiration, to form these molecules which, when the bonds are broken in them, produce massive amounts of energy that your cells then use to power your life.
The entire focus of like the first four major biology classes you take in a biology program are focused at least 50% of the time, on burning this process into your brain. Its super intricate and detailed, involving several cycles like the Krebs cycle and so forth, and honestly, once you've learned it you instantly forget half of it lol. But that's what's going on to power every cell in your body.
Even if these molecules were favored, how does them being forced over and over again lead to replication?
The proliferation of the self replicating molecule is an effect of that molecule coming into existence in the first place. It would have no competition, so once it replicates once, and then again, and then again, it becomes the dominant molecule (with modification) until these molecules start consuming one another, at which point competition comes into play.
So this molecule gets formed a lot--how does that advantage in formation lead to one protein X particle directly affecting the formation of another (Which I think is one of the biggest keyholes in terms of life vs non-life?)...Like is there a release of some kind of smaller molecule which goes around an inspires a new reaction that builds another protein X, and thus releases that molecule again to continue? (Kind of like a proto-RNA)
That's probably one of the biggest unanswered questions that biochemists are still working on. What was the primordial initial self replicating polymer? A lot of people think it probably was some sort of rudimentary TRNA or some sort of reverse transcriptase type molecule, that actually began the process, but we don't really know yet, basically.
Hope that helps. I think I got most of that post covered here. Let me know if you think I missed something important.