1. It should be the same assuming you could efficiently capture and purify the carbon dioxide from the air. Carbon dioxide, the same greenhouse gas that everyone is worried about, is used to carbonate soft drinks. However, compared to manufactured carbon dioxide, I would think that the recaptured and purified carbon dioxide from emissions would be much more expensive to obtain and therefore unsuitable for consumer products.
2. They could possibly be converted to another form, but these processes take energy and are expensive.
3. Most gases dissolve in liquids just like solids (e.g. table salt or sugar) dissolve in liquids (however, there are some notable differences, for example, the dependence of solubility of temperature). Fish respire, for example, by "breathing" the dissolved oxygen in water.
Carbon dioxide is special, in that, in addition to dissolving in water, it also reacts with water to form carbonic acid.
CO2 + H2O --> H2CO3
A salt of carbonic acid, sodium hydrogen carbonate or sodium bicarbonate (NaHCO3) is the main ingredient of baking soda. In the human body, dissolved CO2 in the form of carbonic acid, helps to keep the blood's pH fairly constant.