It is impossible to impose family planning measures on the global population. It has be voluntary, and that means education.
The implementation of the one child per family rule in China has had serious costs for the population - criminalisation, financial penalties,employment termination. It has also led to sex selective abortions, and also to a likely decline in the population, with huge implications for the economy and pensions, tax revenues etc.In India, they tried a sterilisation programme, which had little success. There is clear evidence to show that increasing education and increasing economic wealth are the best controllers of population growth.
As to whether we can feed everyone -I think there have been estimations that, agriculturally speaking, the globe could sustain a significant increase in populations - the Malthusian apocyphal vision is not quite upon us - but there does need to be significant changes in diet, especially in the developed world, if that is to be the case.
And countries do need immigration. The flow of humans around the globe is important, but it will inevitably cause cultural tensions, when indigent populations feel under threat from the immigration.