What happens when their natural habitat is turned into cities and people move into them?
I said I was fine with them being killed within cities and towns. The question in this scenario would be whether sacrificing this habitat for human settlement is justifiable, which depends on different circumstances. There you've also got to consider way more species then just mosquitoes.
And what happens in places like African where humans and mosquitoes have the same natural habitat?
That is a trickier situation. I wouldn't oppose some measures to lower or exterminate some populations of mosquitoes in select places, but the methods to do that would have to be pretty well targeted.
Fastest growing economies don't equal better health systems. It equals better health systems for those who can afford it. One of the by-products of a fast growing economy is a rapidly downtrodden working class. How many children need to die while we are setting up new systems and infrastructure?
While the distribution of wealth is definitively a problem, and getting worse, the fact of the matter is that economic growth means a higher standard of living. While some people are getting a bigger portion of the wealth, everyone is still getting more(Poverty is on a steady decline globally, although a lot of people are still struggling).
How should the malaria carrying mosquitoes be extinguished quickly and efficiently, without threatening other species as well? This does not refer to cities, but their natural habitat.