Good question! Conspiracy theories are, indeed, very interesting cases for epistemologists (philosophers who think about evidence, knowledge, and beliefs). I would say that, on the face of it, and at least in this case: yes, there is something that makes your viewpoint more reasonable. Let's call your theory "A" and your friend's theory "B." What are the implications of A? Just that someone who is mentally unstable and owned a gun committed an atrocity, and the news reported it on the basis of interviews, police statements, hospital interviews, and video footage. What are the implications of B? Obama "orchestrated" the whole thing. Obama and his agents paid off (presumably) hordes of people at the schools, out on fake funerals, tricked or enlisted local police representatives to lie about being there and catching the culprit, deceived or enlisted dozens of professional reporters, and so on, all in the service of...swaying public opinion about gun ownership, even though it is to be expected that an event...

By 'conclusive' argument, I assume you mean some argument that proves, or guarantees, its conclusion. By 'total skepticism' I assume you mean to have no opinion one way or the other at all, or to completely lack any confidence in both the conclusion and its negation. Now, if I understood that right, I think the answer to your question is: by considering arguments that are not conclusive, or don't absolutely guarantee their conclusions. Often, we have arguments that, while not proving or guaranteeing their conclusions, they do provide some good reason to think that the conclusion is true. For example: My dog almost never barks unless there's someone coming; my dog is now barking; therefore, there is someone coming. This is not conclusive, in the sense that it leaves open some possibility that someone is not coming. But it seems unreasonable for me to be totally skeptical, or to have no opinion, on whether someone is coming. Rather, I should be somewhat confident, but not certain, that someone is coming. We...

This is a good, and difficult question. There's no doubt that, in some cases, this sort of objection really is an unfair, unhelpful dismissal. Calling you names ("silly pessimist!") could just be a way to fail to engage with what you're saying. Though that may be what's going on in your case, sometimes such objections actually do have a point. Let's set aside the "ad-hominem" fallacy, whether this is an instance of it, and what that implies, and just consider whether one might have a good point when one objects with something like "you just think that because you're a pessimist." It is useful to compare this with a more straightforward case first. Suppose you think that your daughter is the best singer in the choir, and someone says to you "you just think that because she's your daughter!" You might reply, "but I hear her singing, and I hear the others, and I genuinely think she's got the best voice." "Yeah," the objector replies, "of course you think that, whatever, have fun thinking she's the best!"...