Many of these problems you mention are due to empires past imposing borders that don't correspond to natural nations. Most of Europe's borders are pretty natural equilibriums settled after centuries of wars. They are not perfect though so we are now seeing secessionist movements across the continent. Demographic changes and migrations flows threaten to upset these equilibriums. Africa and Middle East have different problems since their borders are more artificial and imposed from the outside. Most of these regions of the world can barely hold together a cohesive government without outside help.
Global city-states need to become independent with open immigration, separate from the Nations which should enforce strong immigration controls to maintain the native population & culture.
Moore's law has not been an exponential increase in technological capability in general. It has only been an exponential increase in one particular technology - more of the same. I see no evidence that the development of novel technology in general has sped up in any way.
No technology has ever extended life. The so-called gains in life expectancy have only come about by reducing the causes of early mortality and slowing down the diseases of ageing.
I'm not the commenter you're replying to, but maybe they meant that we've only reduced early causes of death like disease etc, but not done anything to affect our internal biological processes that cause aging. As an example, reducing skin cancer by staying out of the sun keeps you from prematurely aging, but it doesn't stop your hair from turning white and your wrinkles from forming.
Drugs that change our metabolism can affect how much damage something does to your body, and you die because your body systems fail or degrade. So fixing some causes and symptoms should be able to increase your possible lifespan. Just like we can increase the lifespan of some simple animals, we could increase our lifespan through physical means. There's no magic spirit inside you that can only last 120 years, as far as anyone knows.