You think a lot, but it all sounds very unscientific and essentially unprovable. It's like saying "I think I have an invisible, undetectable purple dragon in my garage" because your theory lacks any foundation or way of proving it.
1) You're abusing Descartes in ways unimaginable. Read his Meditations: He is extremely sceptical about perception and he claims to have proven the existance of the outside world.
2) Those random generator experiments are all nonsense, and based on selective statistics. Never ever has a controlled study shown any variations in randomness
3) The butterfly effect only works if you're under the assumption that we have free will. Which is a complex question on its own.
Your argument is valid, but keep in mind that what you're talking about isn't science, or even quantum mechanics, but interpretation of QM. It's not proven or anything, it's just the hypothetical/philosophical side of QM. For reference, see the wikipedia article on 'interpretations of quantum mechanics'.
I think this question is muddled with a silly assumption, namely that there is a difference between the physical and the mental. This assumption, of course stemming from the silly Descartes, is the biggest crap people have ever believed in, because it gives rise to all kinds of philosophical and scientific problems, which even Descartes himself knew of. It has no way of explaining how psychoactive drugs work, or how the brain influences the mind, or even how the mind influences the body: How are the two connected? It can't be via physical laws, because the mind isn't physical. The two are posed as separate domains, while they have to be connected to each other.
Either way, if we let that assumption go, we can see that if thoughts are physical, the entire question is nonsense.