Interesting question. I am just throwing out some of my thoughts, I don't know how coherent my post will be.
It seems to me, that the points mentioned in the OP can be classified in two parts: human-related (that would be the conspirary theories) and "super-natural", this would probably need a defintion.
As far as the conspiracy theories go, I believe that there are more things going on below the surface than "ordinary" non-involved people realise. It's probably rather complicated, but I rather doubt that this would classify as "conspiracy theory" as it is commonly understood.
Concerning the supernatural phenomena, I believe that there are things that we cannot (yet) scientifically explain, but mostly due to the fact that our theories are not developed enough or due to the fact, that our measuring tools are not appropriate. As human beeings we have a certain perception of reality, and this doesn't mean that there is not more to it. For example, just because we can only "see" three (or four including time) dimensions, doesn't mean that there are not more. Such things could explain phenomena that we to this day classify as "supernatural" but in reality just escape our perception.
Doing research in pure math, I am aware of the fact that every day new things are discovered in the "mathematical universe". I am certaine that with time sciences (such as physics and chemistry) will pick up these theories, as they have in the past (for example quantum mechanics is built on representation theory, or general relativity is built on differential geometry). They will use them to develope ever more precise models of the universe which might one day explain phenomena that we at the moment classify as supernatural.
It will probably ake a long time. My hope is that in about 200 years physicists will use the theories that we develope today :-)