The Earth is always almost exactly in a radiative balance with space, except on pretty short timescales. If it weren't, we'd quickly cook. The radiation the Earth receives from the Sun fluctuates orders of magnitude more over solar cycles, but it's debated whether that even has a meaningful effect on global temperature.
It isn't. The amount of energy (and raw materials generally) required to produce a given amount of economic output is not constant. It gets smaller as technology advances. That offsets the effect of increased economic output. Indeed, as more and more economic output becomes information instead of physical objects, the average amount of energy required per unit of economic output will shrink even more.
The notion that economic growth can continue without growth of energy is a short-term illusion created by the transition to an information economy, outsourcing of manufacturing, and perhaps a lack of appreciation for the ongoing growth in energy consumption even within countries like the United States as the economy shifted away from physical goods, let alone the growth in energy consumption in countries like China that ramped up physical manufacturing to make this possible.
My phone uses less power then the one I had 5 years ago, as does my PC.
In fact every industrial manufacturing process today is using less energy then it was in the past.
This is because energy consumption reduction due to efficiency improvements goes -- to be very generous -- as 1/t, and exponential growth goes as e^t, and e^t/t is still exponential for large t.
Per capita energy consumption has not been growing in developed countries like the US. It has been decreasing for at least a couple of decades. Total energy consumption has been increasing because of population increase, but that is expected to level off around the middle of this century.
No, it doesn't, because everyone else is also increasing their economic output. Assuming stable population, one individual's share of the energy supply remains constant.
https://www.tandfonline.com/doi/abs/10.1080/1478644960862084...
https://en.wikipedia.org/wiki/Carbon_dioxide_in_Earth%27s_at...