\1. No, we know the the green revolution happened and there was lots more stable food, so population grew.

Climate change is due to increased use of fossil fuels. There are parts of the world that have low density population / high fuel use, such as the United States. Opposite, there are parts of the world with high population density / low fuel use, such as any poor country you can name. Overall: statement is both incorrect and too simple.

Why did the green revolution happen? Going deeper, higher population means local areas start to run out of available renewable fuels (e.g. you chop down your forest faster than it can grow.) The industrial revolution was mostly a search for more fuels. Then someone works out how to turn natural gas into fertilizer and all of a sudden anyone can grow more crops in a given area. More people = more fuel = more food = more people.