There is no solution I can see, and that's worrying. While we're all running around curing diseases, solving global warming etc, the thing that will kill off our species is our own "success".
6. You're expressing yesterday's fear. Population growth in the first world is stable, low, or even negative. We currently have no reason to believe that the third world's population growth won't do the same. Current projections for peak world population are "a little bit larger than now" instead of "trillions and trillions", and the problems of providing for them indefinitely "surmountable".
* Population growth in the first world is stable, low, or even negative.
A quick google search shows that whilst population was pretty stable in UK in the 80s, since then it's been steadily rising. Growth is now 0.75% a year.
The US has a similar story, fertility rate below 2.0 plus migration from the third world results in net population growth, even though the population of the US is no longer "exploding".