That Momoiro Kataomoi is just too cute. Sayu out-Ayayas Ayaya. Gonna really miss her.
Funny that you guys are saying that Crying is an archetypical H!P song. To me, it seems a bit AKB-ish.
Regarding octaves, what claneski says. There may be a song here or there where a portion of a verse is octave doubled but it's not a regular thing by any particular vocalist. Sometimes Tsunku or other backing vocals will be an octave down or up. Offhand I'm thinking of Moonlight Night Tsukiyo no Ban da yo, where large portions of the vocals are an octave higher than the chorus. Honestly I can't really think off the top of my head of any female groups where one of the members regularly sings vocals an octave higher or lower than the rest of her group. I'm sure they exist but doubtful in mainstream pop. There's an 80's song Automatic in which lead singer Ruth Pointer's vocals are an octave lower than the chorus. It's really striking, and would be very noticeable if done in an H!P song.
OTOH there are probably quite a few mixed gender and male only groups that regularly do octave doubling.