Scientists have been studying the burning of fossils fuels, which produces what we call "greenhouse gases". These gases include water vapor and carbon dioxide and are called greenhouse gases because we think that they trap the heat from incoming sunlight in the earth's atmosphere, which heats it up.

Over the life of the earth (which is over a billion years old!) there have been many, many ice ages, when the whole earth was covered in ice and snow, as well as many tropical periods when there were no polar ice caps at all. We know this from the rock record. Currently our earth is right in the middle of a transition-- we're just coming out of the last ice age, but we're not yet in a tropical setting.

As to feeding the world, if sea levels continue to rise due to glaciers melting, lots of low-lying farmland will be flooded so we would have to find other places to farm. If we reduce the amount of greenhouse gas that we produce, we would stop the warming of our atmosphere due to human causes.

Nobody knows. This is the reason for the debate about climate change. The problem is much more complicated than what you mention, however:

1. Even if we humans were to suddenly become extinct tomorrow or be whisked off the planet by aliens or whatever, we've still put an awful lot of carbon dioxide into the air already, and that's going to have some effect on climate. Even stopping fossil fuel consumption right now may be too late to prevent a lot of the changes that are going to happen. In other words, it may already be too late to stop the worst of climate change.

2. We burn an awful lot of fossil fuels doing agriculture. Even if you live your life solar electricity and walking everywhere, there's still the food you eat, which has to be carried from the farms to the markets in gasoline-burning trucks or diesel-burning trains. New engines for vehicles that burn hydrogen instead of fossil fuels might solve this problem, but the engineering isn't there yet. Ironically, the power source for making hydrogen exists, namely nuclear power - but nuclear power has its own drawbacks, namely radioactive waste that takes longer than the lifetimes of civilizations to degrade.

3. Carbon dioxide is known for a fact to be a greenhouse gas, but it isn't the most important greenhouse gas in our atmosphere. That honor belongs to water vapor. However, the amount of water vapor in the atmosphere will increase as temperature increases, causing even more warming, and so on. The worry about carbon dioxide is that it will amplify the water vapor greenhouse effect. It's already doing some of that, but we don't know how much it will do because we're nowhere close to equilibrium. It might be one or two degrees Celsius global temperature change, or it might be five or six.

4. There is evidence that there are natural causes of global temperature rise as well as carbon dioxide levels, and some of them we have no control over (such as changes in the brightness of the sun). We don't yet know how important these factors are.

5. Climate is more than just temperature, but also includes rainfall patterns and things like that as well. This drought that California is experiencing? It might be due to global warming (*might*). Rainfall patterns depend on wind, and we don't know how global warming is going to affect changes in winds around the globe. The outcome is going to be bad for a lot of people, but we don't know how bad, or in what way it will be bad.

6. Plants can adapt to climate change, but only to an extent, and we don't know where that limit lies. We know from fossil data (pollen cores in lakes) that plant populations in the past moved quite rapidly in response to ice age cycles, and those ice age cycles came and went with about the same speed and the same magnitude as some of the worse predicted global warming scenarios - but plants then didn't have human agriculture and other modifications to the landscape to block the way.