Ok...when does this 'anti age' thing start. NOW? So all the useless babies will STAY useless babies forever?
You can't GROW without food, so if we didn't eat we'd be pretty much stuck exactly as we are.
You REALLY want a generation of people who never grow up? And pretty soon the earth would be covered by squishy, crying babies nobody wants. You'd have the current population of adults, and all the never aging infants we produce.
And these kids would never intellectually age, either. So really...useless.
Aaaaand all the people who can't deal with the kids, they spend eternity torturing a baby they don't want? And the kid spends an eternity being ignored and abused? Being immune to physical pain doesn't mean you can't be scared or emotionally hurt.
I can just see people throwing their 50 year old squalling infant against the wall and kicking them around like a football.
I would imagine that it would be alright for the first few hundred years. Eventually, though, I have to imagine that it would become amazingly boring going into the first few thousand. of course I would hope that we as a race would begin to explore interstellar travel. That would definitely add a few thousand more years of entertaining experiences. Still, in the end I have to imagine that it would become amazingly boring and ultimately lead to existence being torture. Who knows, it would be nice to be able to read everything I'd like to read.
Finally we will get into space. If we are immortal we don't need suits, protection, food, water, oxygen, heat and we will have all the time of the world to reach other systems and even galaxies.
If you mean not dying of old age or disease, the answer is pretty much the same. But we would need things like a space elevator, ships, stations and bases. But we would have plenty of time to invent and built those.
If death ceased to exist the biggest problem would be overpopulation and running out of resources to feed and house a growing population, eventually all the world's resources would be used up and the planet would be choked to death by an overabundance of Humanity.
No one would have to worry about starving to death because in your scenario that threat has also disappeared, but eventually all the world's plants and animals would be eaten or destroyed, the delicate balance of the food chain would be broken and the world would die anyway.
But then, considering aging has also been stopped in this scenario, would it be possible for new children to be born at all? The fertilized egg needs to age in order to begin dividing up into the cells that will bring forth a new Human; without aging the egg will go no further then the fertilized stage and eventually get flushed out during the woman's cycle. No more Humans would be born. That solves the overpopulation problem.
But the world is overpopulated as it is right now and it struggles to sustain us and the other life on its surface; the only good thing I could see coming out of immortality is that perhaps with more age will come wisdom in our race and we'll learn how to work with nature to benifit our world instead of against it.