Throwing plastic toys into landfill is recycling, it's just not at the pace some require to offset their upper class guilt. Energy, we'll run out of it when we the sun burns out and we've depleted the other nuclear sources, not by taking stored energy from the sun and burning it to produce a gas that is then recombined with energy from the sun to give us fuel again.
Yes, and the Earth will recycle itself after the Sun runs out of hydrogen fuel.
You're completely ignoring time here. We may never get to recycle the landfill because the pollution will kill us before. Yes, the Earth will clean itself up in a thousand years, the plastics will decompose, and the Sun will refuel the Earth, but those things are irrelevant if humanity is dead by that time. If we want to keep rising the standard of living on the entire planet, we need to stop poisoning ourselves and trashing everything around us in such a stupid way.