Earlier quoted context omitted.
If no one ever died, the world would overpopulate even faster. If nobody ever died, the whole concept of procreation would change profoundly. With first world countries already in zero or negative population growth, creating an infinite lifespan would most likely further that trend. And in any case, we're talking about longevity, not immortality. You can still get hit by a bus.
Doubtful. I envision a "brave new world" styled world. Bunch of people in prime condition, "endless" amount of time to pair with everyone else. I somehow imagine that people will continue to go at it like rabbits.
The stigma around childbirth is a little scary to think about. But all things considered, I think that a society would adapt to limit births by some means if we achieved clinical immortality.
And there are plenty of means to limit birth without stopping sex. Just asking people to sterilize themselves would probably be sufficient, especially since recombinant cloning actually is at least a reasonable thing to talk about with current technology. (Sterilization doesn't mean you can't ever have kids, just that it's going to cost you a fair amount, and you will have a lot of paperwork to do.) The concept of clinical immortality, in contrast, hasn't really advanced beyond the legend of the "fountain of youth."