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This is true but it still kept at 20 million in France even though they had larger families. It was not like they were breeding at 100% capacity and just could not get past 20 million either. The population suffered a huge hit after the black death yet in not long it climbed back to around 20 million and again hovered there.
Longer life will not effect that much in the long term, again I will mention Japan. Many of the resources of the nation are being held by old people so the breeding population is shrinking and so the population as a whole is shrinking. However, this will stabilise one way or another even if that involves large portions of the population ageing and then dying to significantly reduce the population, the younger generations will just expand into the gap left by that and we might just see populations change in cycles with the population getting old and dying off to be replaced by a young population boom in the following years only for them to then die off in 80 years.
Immortality is something different and may actually have an impact. The population will reach the comfort point and if it doesn't stop breeding by enough it might just mean governments have to get involved. But creating a Dyson sphere would not solve this because again, populations like to hover at comfortable levels. So if we made a habitat in which 200 billion could easily live it would not take long at all for that habitat to be filled to 200 billion and then you are back at square one.
Africa could be an issue if they cannot curb that. We don't know, maybe they legitimately just haven't reached the point that they as a society feel they can comfortably sustain(as this changes by the perceived needs of a culture) but it's also possible that they just don't have the control to stop the increase and are just going to perpetually increase forever. Maybe it require a degree of intelligence on the part of the average citizen that they do not yet have.