A space elevator is one technology that needs no huge breakthroughs. We are within an order of magnitude of the required materials science to produce such a thing. The main obstacle is will to do. Given funding and an Apollo type effort, this could be a reality soon, and allow "cheap" access to space.
Africa is mainly a political problem, so I doubt any amount of technology will affect the situation there much. Africa is so far behind current tech that advances here make very little difference there. But current nuclear/solar/other power sources could revolutionize Africa if the warlords ever went away.
As for slavery and civil rights being products of advancing tech, I would tend to disagree. I think it might have been facilitated by advancing tech, but the elimination of slavery was first and foremost a political/social solution. Tech just made up the difference once slavery was outlawed. Try to tell all the estimated 12 million present day slaves (Not talking US here) that modern technology has made slavery a thing of the past.
Current lifespan is due almost entirely to vaccination and sanitation. Neither of those is cutting edge tech. But a large advance in lifespan would have to be technological, not political or social. You have me there.
Medical care is expensive in large part because it is so effective. The more effective the treatment the more complex it tends to be. The higher the technological advancement of the product, the more expensive it tends to be, (computer chips being possibly the only long term exception)
We could solve the fossil fuel problem right now if we wanted to with nuclear power. Fusion would be nice but isn't required. Fission could power the world quite well for a very long time. Unfortunately the greens hate nuke, and you can't do anything in this world without their blessing.
Gross oversimplification here