1. The planet is not a closed system. For what matters the planet has an infinite stream of (solar) energy getting in. So, no, we are not on a finite planet.

2. The plants do a pretty good job with the solar energy, is there some technical impossibility for humans to do the same?

3. Exponential growth can keep going for a while outside of the planet, the universe is pretty big.

Agree: with such a lack of imagination we are doomed.