1. Yes, but in practice people have a good shared understanding of what spam means. Email filters have few problems with defining this. To answer your questions:

1a. No, automated posting is not spamming any more than a mailing list is the same thing as spam.

1b. No, a fan "really eagerly replying" is not spam.

1c. Someone "trying really hard" to sell diet pills can be, you've been too vague to answer there.

Generally, sites impose usage limits on accounts to something reasonable that few people will ever hit organically. Whether you post within those limits using tools or manually doesn't matter. Then the rules say you're not allowed more than a small number of accounts. Anti-spam then mostly boils down to stopping people working around the usage limits.

Musk very obviously doesn't think they're all the same and it's a strawman to claim it is. I used to work in anti-spam and the stuff you're raising is easy. Spam fighting is hard, but not getting distracted by ideological noise that's trying to argue political censorship = spam fighting is really, really easy.