You can't increase the amount of melanin in your skin. It's just that more melanin is seen on your skin when you're in the sunlight to protect it.
There are many supplements that you can take, as well as foods you can eat and some self tanning lotions that contain it.
If you are talking about the solubility of gasses in a liquid then lowering the temperature will increase the solubility of the gas
yes
Photosynthesis is a chemical reaction. Chemical reactions become faster when temperature increases. However, if it gets too hot, photosynthesis will stop.