The song that Rina sings in the opening/ending -- is it an existing pop song in Japan or a song created just for the series?
It's called "Fallen Angel's Love". The music is by Shinobu and written by Masamichi Kaneko.
[Sources: I checked the English version of the ending credits.]
The opening and ending. It looks like it's the theme song
The Opening song, written by Reiji Kitazato, is called "Girls and horny sluts", it's probably most definitely not an existing pop song in Japan. While Reiji Kitazato does music for other (non-hentai) series, like Gankutsuou, this is probably written specifically for this show.