We can grow ten times the food inside that we currently do outside. We can grow it faster, with far greater quality, and with a fraction of the water we use now. And that's before we get into really advanced crop engineering, which is inevitable in the next few decades.
Nuclear power can easily solve our energy problems as desired. If it comes down to it, and there are no other options, they'll turn back to nuclear power. Most likely the radical acceleration of solar will solve half of our energy problem all by itself.
I see no reason why a die-off would occur due to population growth.