My idea is an planet that is one living organism wrapped all around an rocky foundation. It orbits an sun of one solar mass, and has an Earthlike radius. Its albedo is about 20%, so it gets 1098.4 W/m^2 of usable energy, which equates to 2.80X10^17 W of energy. It uses photosynthesis to produce glucose, and synthesizes nitrates to use for amino acids from its atmosphere, as well as recycling its waste. Its photosynthesis is 26% efficient, so 7.28X10^16 J of energy is stored as glucose every second, and every mole of glucose stores 2.88 MJ of energy. That means that every second, 25.3X10^10 mol of glucose are produced, and every second, an equivalent amount is used. The amount of energy it uses in a day is equivalent to 6.29X10^21 J, or 1.50X10^18 kcal, which means that its mass is 5.97*10^21 kg. It has its own atmosphere, which it uses to be able to produce the biochemical reactions it needs to survive, and complex systems to live.
It reproduces by creating 70-kg spores that can survive the vacuum of space, as well as atmospheric reentry, and fires them out at 50 km/s every now and then. Once a spore lands on a planet and absorbs water, it begins to grow until it envelops the entire surface, and begins growing outwards once that is done. It has many long, thin, strong villi that work to optimize surface area for biochemical reactions and light capture, and they work to thermoregulate, seeing that due to internal reactions releasing 64% of their energy as heat, it produces 4.66*10^16 W of heat. The villi can be kilometers tall, and have pockets of hot air that reduce their density, and keep them afloat on the massive ocean that the organism uses. Antibodies break down any organic matter that comes in contact with the surface, preventing infections by pathogens and giving an input of nutrients. Can my living planet exist, with our known models of biology, physics, and chemistry? Why or why not?
For example, how thick can it grow before it becomes too large to support its own weight? And, how much area would it need to stay at an internal temperature of 37 degrees Celsius?