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Earth wouldn't have coalesced without the sun in the middle. Otherwise we'd still be a gas blob.
Nuclear materials were formed in supernovas. They wouldn't exist in the first place without a star.
Well, yeah, sure. But that star is not the Sun.
I mean, sure? It wouldn't be a gas blob, but it would be a very different system. But that still has nothing to do with it -- even if the gravity of the sun influences how the earth coalesces, it's still not where the thermal energy of the core came from. That came from the potential of the dust itself.
Which wouldn't have the potential if the larger sun didn't form first to create the gravity to allow the rest to form.
Star != Sun is just pointlessly pedantic. You're not trying to learn anything, just be a smartass.
This is simply incorrect. The gravitational potential of the body would be there regardless of what else is going on around it. And either way, the OP's question was not about some hypothetical where the sun doesn't exist, it's about where energy came from in the real world.
? The OP's question was literally "is there energy on earth that didn't come from the sun." I am not the one being pedantic here.