1. You want 40w+ per square foot of high quality LED. Maybe even up to 50W because you are running CO2.
2. Whatever fits your budget don't get anything under 2.6umol/J. Floraflex has a new light that's $650.LEDs are getting cheaper at an alarming rate so you almost can't go wrong whatever you can afford.
3. You would need a minimum 60,000 btu and I'd consider bigger even. (Lights alone will be 46,000btu at 50w/sqft)
4. Something in the 165-200pint per day range. This depends a lot on your growing style.
5. For that size grow CO2 burners might be more efficient.But bottles are still doable. Titan controls has a dual tank setup that I think would probably be good so you can run most of the cycle with no bottle change. Otherwise I'd run a burner. But this will add heat and humidity to the grow so you have to account for that.
6. A good AC will control its temps on its own just fine. If you meant grow room controller I personally use Trolmaster. But after installing a couple of them and using for a while I feel like they can do better but most controllers aren't very impressive in general. For that size room probably worth a controller just for the light control alone never mind the other features.
7. Depends on how good of a grower you are. Extrapolate your yields for a 16x16 space by multiplying your 10x10 yields by 2.56.