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Freedom

First, I want to clarify that indeterminism is there exists no fact to the matter about future events. It is different than saying that the future is extremely hard to predict. In other words, some say that a coin flip in indeterministic. However, assuming that all particles (atoms, and molecules, etc) behave in mathematically predictable ways, then an omniscient being, knowing the physical properties of all relevant matter (the coin, air current, force of flip, etc) should be able to predict the outcome. Therefore, a simple coin flip is not evidence of indeterminism, because its out come is theoretically (though not practically) possible to determine. Is this a correct way to interpret the view? Second, where do indeterminist think that indeterminism can come from, given the standard view that all matter follows predictable laws of physics?

I don't work on these things myself, but I'll make one point quickly. Nowadays, it isn't at all obvious that you could predict what will happen when the coin is flipped if you knew all the relevant physical facts about the present, for the simple reason of quantum indeterminacy . It may be that the current physical facts make it overwhelmingly likely, say, that the coin will land heads. But quantum mechanics tells us that it is possible, still, that, when you flip the coin, it will turn into a dove and fly away, let alone that it will land tails. So many people think that physics itself speaks against determinism, not in favor of it. Not everyone, mind you, but plenty of people.
Freedom

Everything can be determined. Therefore, the world is deterministic. What do you think? (1) Everything can be determined. (2) Determinism is the thesis that everything can be determined. __________________________________________________________ Therefore, (3) the world is deterministic. For example, suppose I am raking the leaves outside my house. Then the fact that I am raking the leaves can be determined. It can be determined by anybody driving past my house. It can be determined by a high resolution satellite (on a clear day with no overhanging trees). It can be determined by merely witnessing me raking the leaves. The same goes for anything else that happens. Its occurrence can be determined. For (1) not to be true would be to undermine the assumption used in court trials. All court trials assume that the occurrence of anything, crimes included, can always be determined (even if not by the available evidence). For (2) not to be true would be to say that there are things that cannot be...

As the Stanford Encyclopedia article on the subject defines it, causal determinism "is, roughly speaking, the idea that every event isnecessitated by antecedent events and conditions together with the lawsof nature". This is a much stronger claim that is made at (2). To say that "everything can be determined", in the sense in which that phrase is used at (1), seems to mean just that every current fact can be known, i.e., can be determined to be true by some sort of ideal observer. That is itself a very strong claim, and not one that is obviously true. (Can it now be known what the temperature is inside some star millions of light years from here? What about facts in the past?) But even if it is true, that does not show that, to use your example, your raking the leaves now was causally necessitated by past events.
Freedom

Of the many strong arguments against free will, I find the following to be the most convincing. Some theorists have suggested that free will seems to require one to be responsible for the way one is, "mentally speaking." For example, in order to be responsible for my decisions, I must have chosen, in a conscious way, to be in the particular mental state I was in at the time of my choice. Hence, free will seems to require preconsciousness; but this can be pushed into an infinite regress. Do you know of any possible answers concerning this argument?

The obvious response is that this premise ...[I]n order to be responsible for my decisions, I must have chosen, in aconscious way, to be in the particular mental state I was in at thetime of my choice. is one we have little reason to believe. I don't see any particular reason to suppose I should bear no responsibility for my current decisions even if my current mental state was determined by causes outside my control. Perhaps one wants to say I'm not "ultimately" responsible, but then the question is why free will should require "ultimate" responsibility in that sense. These kinds of arguments often trade upon this kind of ambiguity.
Freedom

If quantum indeterminacy is true, it proves that we do not live in a deterministic world. But I seem to have trouble with the notion that indeterminancy give you responsibility for your actions and decisions. For example, I am walking into a store and I open the door. There is someone behind me. I can hold the door open for them or I can keep on walking. If quantum indeterminancy is true, than I have the possibility to do both. But am I truly the author of the decision or was the decision ultimately made by something which I had no control over? And is it intelligible to say that the former is even possible?

For this reason, many philosophers now suppose that the problem of free will really has nothing to do with determinacy. My own favorite book on the subject is Daniel Dennett's Elbow Room , but I'm sure other people have other favorites.
Freedom

If, through free will, we take only those actions that we choose to take (barring physical enforcement or life/death situations), then where does the concept of 'external influence' fit in, and are we not then ultimately accountable for all the decisions we make in life, even self-destructive ones (the battered wife, the addict, the gangbanger teenager, etc.)?

I don't see how the conclusion follows. Coercion is an obvious counter-example. If someone holds a gun to your head and so coerces you, say, to make crank phone calls, I don't see that you should be held "ultimately accountable" for upsetting the recipients. And coercion hardly has to be "life or death" or even physical. But once you've allowed that much, then it's easy enough to see how external influences might have an effect. In very simple terms, what coercion does is change the costs and benefits of different actions. It seems obvious that external influence, such as addiction, can do the same thing. (I'm really not sure what you have in mind vis-a-vis battered wives. But how can we toss that in when we're supposed to be waiving physical coercion?)