I read somewhere that it should be το κορίτσι τού (with an accent on τού) to differentiate between 'the girl reads him a book' and 'his daughter reads a book'. So is the accent mandatory or optional?
Του is normally not accented. It is, though, if it is a personal pronoun and can be mistaken as possessive in the context it is in. So, in this sentence and unaccented του would mean "his" as a possessive whereas an accented τού means "(to) him".
It's either the genitive weak form or σε+strong accusative form for the indirect object. The tips¬es are poorly made on that matter. I'll tend to it. Sorry for the inconvenience... :)