I think that if a serious extension of life becomes a reality, it will be very expensive. Otherwise, it is necessary to limit the birth rate, or even forbid people to have children.
Not necessarily. If humans can become truly immortal, we could explore the entire galaxy and believe me, we have plenty of planets there to live and spread, we wouldn't need to stop having children at all.
This looks like a better idea than limiting the birth rate. Besides, I know people keep working on it and it's just a matter of time when we are able to leave the planet and start living somewhere out there on another planet.