> Has it yet been absolutely proven 100% that a gas comprising 0.04% of Earth's atmosphere is the main culprit/control knob which controls climate(s) around the Earth?
Aside from the hyperbole, pretty much yeah.
Oxygen and Nitrogen aren't important when considering the greenhouse effect since they're diatomic molecules with tighter absorption bands and don't have the broad bands in the IR so that 99.96% of the atmosphere just doesn't matter (Argon is monoatomic which is even more dismissable. H2O matters but gas-vs-droplets is complicated and took decades to sort out).
It is all the rest of it that matters. And for example, satellite measurements of the absorption bands in the atmosphere show that CO2 absorption has been widening which explains the satellite observed reduction in IR emission from the Earth which explains warming as an imbalance in the heat budget of the entire planet.
The increase in CO2 coming from humans is also established via analysing the isotopes of carbon in the CO2 in the atmosphere and we can see that it is coming from carbon that we dig up out of the ground (protected from cosmic ray radiation) vs. the CO2 that was in the atmosphere. We can also measure that only about half the carbon we emit stays in the atmosphere, while the other half does get captured by the natural carbon cycle. But that's enough to disturb the balance. Small deviations in the budget add up over time.
And these questions are very, very basic. We wouldn't be discussing climate change if scientists didn't have the answers more or less nailed down.
More information and a massive amount of references can be found at skepticalscience.com
I'd also recommend Ruddiman's undergraduate text on climate:
https://www.amazon.com/William-F-Ruddiman-Earths-Climate/dp/...
Although for $287 for the paperback, maybe rip it off on libgen. I think back when I bought the first edition it was $80 which seemed steep. Fuck science publishers, seriously.