Once you use the energy and it turns into heat, you can no longer use it.

First, heat is energy. Second, you can use heat as heat. Third, you can use heat to boil water to turn a turbine to create electricity, which you can use to do very many things, including create heat.

No, you can't do that. If you could do that, you could build a perpetuum mobile.

Yes, you can: https://en.wikipedia.org/wiki/Waste_heat_recovery_unit

Now, whether we can effectively use the energy is an entirely other question. There's plenty of technical limitations. But in a closed system there's no reason an object cannot have perpetual motion with perfect energy recovery. Of course, closed systems don't help us, because they cannot exert useful work outside of the system.

You can't. You can increase the efficiency that way, but you can't use it to produce limitless energy. We wouldn't be burning fossil fuels if that was an option.

You're not "producing" limitless energy. You're reusing the existing energy, because the energy cannot be destroyed. Again, there's no reason why this can't be done within a closed system, except for our technical limitations. Indeed, tracking and recovering energy is the entire idea behind reversible computing.

https://en.wikipedia.org/wiki/Reversible_computing#Physical_...