Credit where it's due: this is based on an original idea and draft by Penton, but I revised and remade it so thoroughly that he said I might as well post it myself.
Notice the confusion about whether Dr Wondertainment is male, or female, or an organization. That's deliberate; in fact, Headless isn't capable of understanding that it's even a question. Consider the phenomenon of tautomerism, and how it might apply to identity.
The thing about years: Headless (as do most, if not all, of the other Little Misters) lives through years several times each, and not necessarily in order. He has no idea that there's anything unusual about this; doesn't everyone do it? How else can you be in more than one place at a time, and do more than one thing at a time? Although lately, it seems to have stopped happening… and if you were to ask the other Little Misters, they'd agree that the last few years have all been consecutive, and only once each, and isn't that strange?
Note that odd naivete about the world. It's not just that he doesn't know the word 'gun', he's missing other details too. But what can you expect of someone who spends >99% of his life in attics and closets and storage compartments?