The last time there was a "population crisis" fertilizer was invented the problem vanished. Currently GMOs have shown they produce massive improvements in yields and we're still in the early phases of this research. So it isn't exactly naive to think that this won't be an issue (though I'm not saying you should completely dismiss it).

As for land, well Europe is the same size as America and has twice the population. And neither have anywhere near the density that China or India does. So there's quite a bit of evidence that we shouldn't be overly concerned about these issues.

And what looks like the best way to solve them is by helping other countries develop more rapidly (which is actually a bonus for tackling climate change too!) but this is a pretty unpopular opinion.