Just a few thoughts, since I entertained this theory once; and I like Sara so it's relevant to me. Disclaimer: my current recollection of past events is weak, so some things may be wildly inaccurate.
I agree it's likely Nozomu isn't a teacher, and consequently, Sana's father (there's also how Pegasus probably isn't HOPE, at best an aspect or offshoot). But Nozomu, in my eyes, definitely isn't a "normal guy"; the dude is almost certainly a freak (all minimally significant characters in this game are, even Karin! Maybe Haruka's husband isn't, though).
Ami probably didn't know him very well (he's decent in her eyes, but compared to her mom, whom she holds in an absurdly high, borderline fanatical regard, he's probably akin to garbage), and being fair, her notions of what's "normal" and "acceptable" are far removed from what's generally considered normal by most of society. If her father was a teacher, she likely doesn't even care to mention that fact because he's painfully mediocre compared to her mother. Ami is talented, Sekai is even more, and Akira is to an unknown extent. To Ami, poetry is perhaps the most valuable and beautiful skill.
Rain King:
AMI: "My dream job?"
AMI: "That’s a good question. I’ve always just kind of assumed I’d be a housewife."
AMI: "But I think...if I got to choose anything in the world..."
AMI: "I’d be a teacher — just like my mom."
I mean, we already have a weird rapist god called Nozomu (fleshlight god), and Sekai had mentioned her husband was rough with her. Sekai strikes me as someone who wouldn't lie or try to make up a story about such a thing merely to make Akira jealous (hurt him). I think it probably happened frequently. There's also how "Nozomu" means "Hope". There are some connections between HOPE and Sekai.
Concerning your points: