Ranma wears a wig of dark blue/purple hair. This is a homage to Shampoo, a love interest of Ranma.
Akane has a lot of piglet toys in her room, and one of them is black. This is a homage to Ryoga Hibiki, Ranma's rival for Akane; he was cursed into a black piglet and was adopted in that form as Akane's pet.
Kasumi has a cookbook for okonomiyaki, a Japanese pancake dish. This is a homage to Ukyo Kuonji, an okonomiyaki chef who is a love interest of Ranma.
The camera Hikaru uses is a Canon EOS DSLR.