>do you believe in anything that can't be proven logically
Anything can be proven logically.
>that the world exists to be used by humans?
It just exists. Until some other sapient critter comes along, humans are the sole deciders on the "purpose" of anything, including the Earth.
Is it a good survival strategy to decide the purpose of the Earth is to be "used" by humans? Probably not.
>that happiness is the goal of life?
The goal of life is whatever you set it as. Albeit that goal will inevitably be influenced by others who came before you, and others will attempt to use for or adopt you to their own goals.
You've evolved in such a way as to survive long enough to maximize the potential to pass on your genes, but as genetic evolution has been left in the dust by informational evolution (and CRISPR is on the horizon to boot), at this point, breeding is just maintenance, so even your core instinctual goal is largely irrelevant. I suppose one must aim higher now, nor not, as one would choose.
>in good and bad?
Social constructs are a thing, yes. I doubt there's any supernatural arbitrator outside of mankind though, and if there is, it probably would be alien to our own opinions.
>that humanity is a force for good?
If survival of the story of life on Earth beyond this inevitably doomed biosphere is "good", then yes, I believe we are the last, best hope for that. There's only a billion years left before this place gets so hot that the oceans will be gone (regardless of anything we do). Anything that wipes us out to make room for another species to evolve enough to have a chance to do what we can, would have to be so severe as to give life such a setback that it probably won't be able to do so before it is too late.
But when it comes down to it, even the existence of life being "good" is a matter of opinion. Still, gotta set your axioms somewhere, and it's a widely accepted one - those who think otherwise have little say in the matter anyways.