Searching for Neville's Toad
Hey there! OK, the Head Boy and Girl Duties.
The only references I can find is when Hermione says that the prefects get instructions from them on the train, and also when Percy and his fellow Head Girl keep an eye on the students after Sirius's break-in.
What duties do you think they have?
In most fanfiction, they patrol in the evenings and plan balls, Hogsmeade weekends, etc.
banner by Annalise28
Setting Off Fireworks in Potions Class
Head Boys and Girls lead and supervise prefects, and I suspect they have regular meetings. Aside from that, I think what you said covers their other duties pretty well.
Tim the Enchanter
I think in most Muggle schools, the position of Head Boy and Girl is just ceremonial; there isn't any real duties that go along with it, they're just glorified prefects really. At my school it was just something that'll look good on the CVs. I imagine that at Hogwarts it would be the same. They'd be in charge of the prefects, organize patrols and perhaps be general role models to the other students. Maybe they get certain priviliges, like extended curfew.
They could have been responsible for scheduling of Hogsmeade weekends, though we perhaps might have heard about it in the books, but I certainly don't think they'd plan balls. Hogwarts has just the one ball, and that's the Yule Ball that goes hand in hand with the Triwizard Tournement. Proms and stuff have only recently become popular in the UK, so it's unlikely that Hogwarts would have had any other balls.
Wonderful avvie by psijupiter. Totally brilliant and amazing banner by Julia/the opaleye!