Yep, that's the one. I knew someone who would name his kids Nathaniel and Superfly would get it. (For the curious,
the lyrics -- which are, however, no substitute for hearing Al sing it.)
On the other hand, the first two bits you quoted weren't references. The Avril scene has three quotes from her songs, so that just leaves one reference unaccounted for. It's late in the fiver and will be obvious to anyone who knows the (very 80s) song.
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FiveMinute.net: because stuff is long and life is short
[03:17]
FiveMinZeke: Galactica clearly needs the advanced technology of
scissors, which get around the whole "yanking on your follicles" problem.
[03:17]
IJD: cylons can hack any blades working in conjunction