I think both arguments can be analyzed as inductive arguments and still distinguished in terms of their quality. The book argument is a stronger inductive argument than the coin-toss argument for a simple reason: the probability that Smith's book C is great isn't independent of whether Smith's books A and B are great.
That is, Smith's having written great books A and B makes the probability that Smith's book C is great higher than it would be had Smith not already written two great books. Important: higher than it would be otherwise, which needn't mean higher than one-half. Even though Smith's track-record raises the probability that book C is great, the track-record needn't make it more probable than not that book C is great.
By contrast, the probability of tails on any given toss of a fair coin is independent of whether the coin came up tails twice already: that history of tosses neither increases nor decreases the probability of tails on a third toss.
First a terminological quibble. By "scientifically impossible," I take it you mean "technological infeasible," i.e., impossible given the limits of current technology. As I see it, what's scientifically possible or impossible depends only on the laws of nature, which are standardly taken to be unchanging over time (or at least over any time that humans will experience). I think the jury's still out on whether backward time-travel is scientifically impossible in this latter sense.
To your question: I think there's something self-contradictory in the idea of "correcting what you did" if that means "bringing it about that you never did what you in fact did." Either (1) you did it, or (~ 1) you never did it. I can't see how any consistent story features both (1) and (~ 1).
In that sense, then, there's no such thing as (2) "going back in time and changing things in reality" and therefore nothing that's the "same as" (2). See section 1.2 of the SEP article on time-travel.
Typically, a libertarian (in the domain of politics; "libertarian" is also the label for someone who adopts a view in philosophy of mind or action theory involving free will) is someone who believes that societies should have a government that is the smallest possible in order to protect certain basis rights (perhaps a proper government should, on the grounds that persons have the right to life, prohibit murder and seek to prevent it). A libertarian might (on rare occasions) support some publicly funded health care, but he or she would (ideally) like such matters to be funded by individuals voluntarily by the individuals themselves. So, what about libertarians and suicide? If the libertarian believes that a minimal government should prohibit and prevent murder and she believes that suicide is wrong because it is a case of self-murder, then she may consistently support the government's prohibition and prevention of suicide. However, she may be "opposing suicide on" different moral grounds, e.g. she thinks it is prohibited by God or she thinks that in almost all cases suicide is ruled out on Kantian or utilitarian grounds. For the most part, libertarians do not think these religious or philosophical judgments of these kinds should be employed by the state to control its citizens. So, in this case when suicide is deemed wrong but not as grave a wrong as murder, a libertarian may well contend that suicide is indeed wrong (persons who commit suicide are doing something morally wrong), only adding that it is not within a government's right to make suicide illegal.
There is one additional side to things: while a libertarian may oppose there being an overall, federal government that makes suicide illegal (assuming suicide is not self-murder), her moral objections to suicide may motivate her to join a society voluntarily that makes suicide prohibited. Without knowing the details, I imagine that most Christian monasteries and Muslim communities have rules that forbid suicide (e.g. they would not fund or support the "physician-assisted suicide" of one of its members). A libertarian might join some such organization while still not supporting a governmental prohibition of suicide.
Good question, and as fundamental a question as anyone could ask. I think that the laws of logic must be not only independent of human minds but independent of any minds, including God's mind if such exists. At any rate, I don't think anyone can see how it could be otherwise.
To say that the laws of logic depend on human or divine minds is to imply that the following conditional statement is nontrivially true:
If (1) human or divine minds had been different enough, then (2) all of the laws of logic would be different from what they are.
(By "nontrivially true," I mean that the statement is true not merely on the ground that (1), its antecedent, is logically impossible. If (1) is logically impossible, then the conditional statement is trivially true, even if (2), its consequent, is also logically impossible.)
We can't make sense of the italicized statement without presupposing that (2) is false. If the italicized statement means anything, then it doesn't mean this: If (1) human or divine minds had been different enough, then (~ 2) not all of the laws of logic would be different from what they are. But, of course, my assertion just now about the statement's meaning itself depends on holding fixed at least some of the laws of logic, i.e., it depends on presupposing (~ 2) even on the assumption that (1) is true. Therefore, we understand the italicized statement only if we presuppose that it can't be nontrivially true.
As for the nonphysical existence of the laws of logic, you might look at what I wrote in reply to Question 24874.
I'm going to refer you to two websites. At the PhilPapers Survey, you'll discover that only 4.8% of "target faculty" said that they accept or lean toward skepticism. Among specialists in epistemology (the theory of knowledge), that figure increases to 9.4%, but it's still small enough to suggest that philosophers in general don't think of skepticism as having the upper hand once the reasons for and against it are examined carefully.
For detailed discussion of your second question, you might start with the SEP entry on "Certainty". I hope you find these resources helpful.
On this question, I doubt I can do better than to recommend to you an excellent article written by Professor Donald Hubin, available at this link:
I hope I don't come across as pedantic, but I think that your questions may contain what philosophers call "false alternatives."
First, there's a sense in which both A and B can be correct. It might be that B is well-advised to try a particular something before rejecting it because the risks associated with trying it are small compared to the possible benefits. Nevertheless, it could be true that B "shouldn't have to" try something before rejecting it: that is, B might well have the right to refuse to do X even if he would be well-advised to do X.
Second, C can help convince B to try the thing even while C lets B make his own choice. As I see it, giving B convincing reasons to make a particular choice needn't mean depriving B of a choice -- including a free choice -- in the matter.
I think it does, or at least I think the burden of proof is on anyone who says that "exist" is systematically ambiguous, meaning one thing when applied to numbers and another thing when applied elsewhere.
It's widely held that abstract objects such as numbers, if indeed they exist, don't exist in spacetime, whereas concrete objects such dogs clearly do exist in spacetime. But that doesn't affect the meaning of "exist" itself. In particular, it doesn't imply that "exist" means "exist in spacetime." Otherwise, the expression "exist in spacetime" would be redundant and the expression "exist but not in spacetime" would be self-contradictory, neither of which is the case.
Analogy: It's a fact that some things exist aerobically and some things exist anaerobically, but that fact doesn't tempt anyone to say that one or the other kind of thing doesn't really exist, or to say that "exist" just means "exist aerobically." So I see no reason not to say that numbers, if they exist, exist nonspatiotemporally, whereas dogs exist spatiotemporally: the adverbs differ in meaning, but not the verbs.