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The game text itself suggests how to unlock most songs. So if you can't read JP here's what they say.
Song 1-12: Basic songs (unlock with 4k of points)
Doing any correct motion during a dance gives points. These stack and are never wasted. Every 4k or so points (you should get a number after a dance) you'll get a new basic song.
Song 13-20: Alternative Stage songs (unlock by playing the newest song)
Once the first 12 basic songs are unlocked, and you have played each of them at least once. Points seem to no longer be an issue. The alternative versions of the songs are unlocked simply by playing the newest song once. The next 8 songs are alternate stage songs.
Song 21+ These should be the All Stars Movie Songs
The helpful game text is no longer helpful here. Perhaps a certain number of accumulated points or score on each song? Anyone unlocked these yet?
Yes, you need an account to watch videos. Though, registration is quite simple these days, as there is an english version of the registration page. Two years ago there wasn't, and people had trouble registering.