And they do so at the cost of the environment. Life decreases its internal entropy by increasing that around it. We can build a house, which is a lower entropy state than a pile of lumber and bricks, but we do so at a cost, and that cost is to increase the entropy of the environment.
Same thing within our cells. Inside of a cell is a pretty low entropy place, but it gets there and maintains that state by using energy in ways that increase the entropy of the environment.
No, the Earth cooling does not reduce entropy. A hot object in a cold universe is at lower entropy than a cool object in a cold universe.
It’s in the materials that used to be a planetary nebula, which was much lower entropy than their current state all bound up into a planet.
The light coming off the sun is pretty low entropy. When it hits the moon, some is reflected, and some is converted into heat which is radiated at longer wavelengths. The same amount of energy leaves the moon as it receives, but some of it is in the form of more lower energy photons.
However, when that same sunlight hits a plant on Earth, that plant absorbs the sunlight, and over processes and time, (and animals eating and excreting it) eventually emits that energy again, but in even lower energy photons as what is emitted by the moon.
The sugar and oxygen that your body uses was produced by photons that left a surface at nearly 10,000 degrees F, and when you use that, you then emit that energy at under 100 degrees F. Far more photons at a much longer wavelength.
The Earth creates more entropy than a similar sized ball of rock would. The planet would reflect more light at shorter wavelengths and lower entropy than it does with the life that is present on it.