When I look at these kinds of arguments, I can always tell that they will fail even without reading the argument itself. I do have to read the argument to find the details of how they fail. That the arguments will fail, however, can be seen before reading them.
It's a general principle of logic. Perhaps it is also a general principle of life, but it is specifically, a general principle of logic. Roughly speaking, that general principle says:
There is no such thing as free lunch.
In logical terms, the principle is that a conclusion can never yield more than is already implicit in the premises. All logic can do is rearrange the assumptions, so as to make more obvious part of what was assumed. Perhaps it is because of my background in mathematics, that this principle of logic is particularly apparent to me.
If a logical argument assumes nothing about the world, then it cannot logically derive any conclusions about the world. At best it can come up with some esoteric relation between logical connectives (the sort of thing that turns people away from mathematics).
When we see one of these arguments that purports to reach a conclusion about reality (such as that God exists), but without using any evidence, then we can immediately know that the argument smuggles in some assumptions about reality, and is using those hidden assumptions as the basis for the conclusions. So the way to examine the argument, is to look for the hidden assumptions.
Typically, in these arguments, the hidden assumptions are in the form of very general statements perhaps described as first principles. And then the argument proceeds to supposedly deduce a very specific conclusion from the very general assumption. The trouble here is that the very general statements are often only true in a very general sense - as a kind of broad average way of looking at things. If you try to pin them down to detail, then their truth becomes questionable. For example, look at premise 2 of syllogism 2 in the OP: "Everything that happens/starts has a cause." That's a good general statement that summarizes how things normally look to us. But when you get down to specifics you find that quantum physics does report spontaneous (i.e. uncaused) events. The thing to remember about logic, is that the logic requires that a premise not merely be generally true as a statement of what is typical. Rather, the logic requires that the premise be absolutely true in all details and in all relevant applications.
There's a general class of paradoxes, known as the Sorites paradoxes, that illustrate what can go wrong when you base an argument of statements of general truth that fail to be true in all details. See the wikipedia entry or the SEP entry for examples and discussion.
Looking at the arguments in the OP, they are all of this kind. The second and third use general assertions about cause as their starting assumptions. The first uses a general statement about entropy ("entropy always increases") as a starting assumption.
Even without the evidence from quantum physics, we could look at assumptions of the form "everything has a cause", and we ought to realize that this is at most a general observation and not anything that we can prove.
The entropy assumption has similar problems. For all we know, there might be processes acting in the universe that tend to reduce entropy, in such a way that they counteract the general tendency of entropy to increase. The observed expansion of the universe might be reducing entropy. Or the total universe might be infinite, so that you can always keep the entropy down by pushing it somewhere else - that's like the way that there is always room for more guests in Hilbert's Hotel.
When you see arguments that seem to assume little, but prove much, it is time to be skeptical. Always remember that there is no such thing as free lunch.
Straggler writes: Hmmmmm you seem to be presenting an argument that assumes little but proves much........?
Then it is time for you to be skeptical.
Straggler writes: I agree with the sort of principle you are stating
At least you got that part right. I wasn't making an argument - I was presenting a statement.
Obviously, people are free to ignore my statement. And, obviously, many will. I don't expect bogus arguments to suddenly stop coming.
What always amuses me, is that the people who I see presenting these arguments seem to think that they argue for the Christian god. But if the argument actually worked, it would make as strong a case for Thor or Zeus or the deist's god, or for the IPU or the FSM. I expect the presenters often know that, but they try to avoid publically admitting to that flaw.
PrinceGhaldir writes: About your quantum physics, a piece out of: "In Defense Of The Kalam Cosmological Argument" by William Lane Craig
"The central point to be made here is that the quantum mechanical vacuum on which [virtual particles] depend for their existence is emphatically not nothing. The dynamical properties of vacuous space arise out of its interaction with matter and radiation fields, in the absence of which 'this dynamism of empty space is but a formal abstraction lacking physical reality.' The quantum vacuum is a sea of fluctuating energy which gives rise to virtual particles. Thus, virtual particles can hardly be said to arise without a cause"
The fact remains, that radioactive decay meets all of the tests for randomness. And that's pretty strong evidence that each decay event is uncaused.
PrinceGhaldir writes: But if the universe is expanding for an infinite amount of time, the universe would be infinitely big.
That does not actually follow. After an infinite amount of time has elapsed, it might be infinitely big. But that point is never reached.