To say Daniel just doesn't take meds he is surprisingly cogent. I don't think he has schizophrenia proper, just a raft of issues that make him schizo. But I think he was always going to have issues, being born microcephalic (I'm not sure what his mother did during pregnancy or the quality of her character beyond random internet rumours).
I don't think he's schizophrenic either. Schizotypal, maybe, but that's a personality disorder, not a mental illness like schizophrenia and it doesn't respond well to medication, so if he's not taking his meds that's why he's as functional as he is. He's prone to fantasy and delusion, but you don't have to be schizophrenic to have those, and whilst he's paranoid, you have to bear in mind that
he really is being gangstalked and people really are plotting against him behind his back. Like Fox Mulder once said, "Just because you're paranoid doesn't mean they aren't out to get you". He's never mentioned hearing voices or seeing visions. Ironically, he also speaks far too lucidly to be an unmedicated schizophrenic. What he says is often delusional, but it's comprehensible.
Schizophrenics are unmistakeable. Terry Davis, John Bulla, Alex Knapik-Levert, that guy I can't remember right now who thinks aliens talk to his teeth and thinks he's the rightful King of America. Their delusions are incredibly grand and involve vast conspiracies, the reptilians are using chemtrails to make the 5g towers steal people's souls and sell them to Xenu and replace them with robots*, that sort of thing, and they are prone to stream-of-consciousness rambling and scattered, incoherent thought. Dan doesn't do that, he leads a childish fantasy life where he's a big pop star, the way a lot of 6-year-olds do. Thing is, most 6-year-olds aren't indulged by dozens of adults and have parents to keep them grounded in reality, or at least separate playtime from real-world time.
*Philip K Dick was a paranoid schizophrenic, and it's the major inspiration behind a lot of his work. What if people were secretly robots, and didn't even know it? (Do Androids Dream of Electric Sheep?) What if there was a big conspiracy by godlike beings to ensure that the entire world's history went to plan? (The Adjustment Bureau) What is psychics could see the future and get you arrested for crimes you haven't even committed yet? (Minority Report). What if you were secretly someone else but you had false memories implanted because you're a deep-cover secret agent? (Total Recall) Those are schizophrenic ideas. Dick had addiction problems, tried to kill himself a couple of times, heard voices and kept hallucinating prophecies.