Pretty much every modern estimate I've ever seen suggests around 9 billion people by 2050, with population growth getting slower and slower, probably approaching some kind of asymptote at between 9-10 billion people.
Total Midyear Population for the World: 1950-2050 World Population Prospects: The 2004 Revision Population Database Worldmapper: The world as you've never seen it before
We owe far more of our economic success to the free market than to protectionist or imperialist U.S. tendencies. In fact, on balance we'd probably be better off without all that baggage. And so would the rest of the world.
Global warming will have to be dealt with, but this isn't strictly a problem of population. Per capita, the average U.S. resident emits 20 times (carbon) what the average Indian does. Admittedly, Indians are rather poor compared to us, but money doesn't always buy happiness, the adage goes. Cost of living is also commensurately lower for them. Our entire infrastructure is carbon based here in the U.S., but it needn't be so long-term. Technology is being developed that will enable us to transition away from rampant carbon emission, and new infrastructure will steadily be deployed in the developing economies that will enable them to continue growing their GDP' without growing their carbon emissions. This is all off in the future, however, probably by a decade or two. We'll see CO2 concentration in the atmosphere rise to probably 430-450 ppm before we see a negative second derivative on the concentration curve.