one of the best parody anime in the entire world with the added bonus of having one of the best opening songs in all of anime as well. Coincidence? I think not.
While choosing your pic you seemed to have missed the hyper cute moe Caster folder and hit the Tsukihime one. It's a common mistake.
No, it's a light-hearted comedic spinoff. There's no such thing as a "self-parody," and if you insist on claiming that there is, then I challenge you to name one from something that isn't japanese.
If you'd bother to follow any of the links that that provides, you would find that all of the examples are in-universe references or nods, not full-fledged parodical works.
>CP parodies south park
>this makes it a "self-parody"