Surprisingly little of it comes from water either, at least if you only count dry biomass. The hydrogen in biomass comes from water but the carbon and oxygen come from fixing CO2, and since H atoms are so light they count for very little of the biomass.
I don't know the details but I think it's one of those cases of classical physics not really being able to explain it satisfactorily. Like classical physics falling on its face when trying to explain a light switch: there's no way that classical electrons can jump the gap.
Not using this medium, I'm afraid. You could research the differences between classical physics and ideas like quantum mechanics and relativity. My understanding is that quantum biology explains photosynthesis far better than classical biology. There are probably few who understand it fully.
Sure - photosynthesis takes carbon and oxygen from the air, plus hydrogen from water, and turns it into sugar. The remaining oxygen from the water gets released into the air as O2. Proteins and DNA and all the other molecules in the plant are made from that sugar, plus trace nutrients from the soil.
Sure, but by mass it's not very much. Most of a plant's dry mass is carbon and oxygen, and that comes from air. This is why plants generate soil in the long run, instead of using it up
Yes, the more precise statement would be that wet plant biomass is about half air and half water, plus a few percent nutrients from soil. But biologists usually think in terms of dry biomass, and that really is mostly made of air.
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(Plus hydrogen from water and a small amount of nutrients from soil, which make up only a small fraction of our mass but we can't live without them.)
The carbon that makes up the bulk of their matter is pulled from carbon dioxide in the air.
I can't help with the quantum mechanics part.