This is a hastily-assembled 8th style CS info page.
You can get Extra stage and One More Extra Stage in arcade mode like in the Arcade version of IIDX 8th style. To get the Sakura extra stage, you appear to need to pass a 7 star song on HARD with an A. To get One More Extra Stage, you appear to need to pass Sakura[A] with an A on HARD - this lets you play Xenon.
Note that you can play Xenon and Sakura whenever you want normally; this procedure just unlocks the Sakura and Xenon extra stage backgrounds for gallery mode.
There is no song records mode; there are only records for arcade modes. Song record information is shown on the song selector (by pressing start, then select).
8th style has folders, kind of like Pydance or Stepmania, in the song selector so you can look at a subset of all available songs. The folders are All Songs, New Songs, Old Songs, Not Cleared, Not Cleared (Hard), Not Played. There is also a folder for songs that you've gotten a specific grade on (e.g., "DJ Grade AAA"). There are also several sort options: sort by title, difficulty, play count. Finally, you can have the score counter at the bottom of the screen display EX score instead of money score by selecting the "EX score" option below the sort options in the song selector.
(Konami new songs introduction coming! It'll be up before 30 Nov, I promise.)
New songs for IIDX 8th style CS:
Spiral Galaxy (by DJ Setup), 太陽〜T・A・I・Y・O〜 (Naoki feat. Hoshino Kanako), and Don't be afrid myself (platoniX with ray.D) have been identified by players as unlockable songs so far.
To unlock Spiral Galaxy and TAIYO, you need to clear all the new songs. You can do this in Light 7 if you want; difficulty level doesn't matter, you just have to pass it. Ideally, both will unlock at the same time. If you only get one, keep playing and you'll eventually get the other.
Gigadelic.net is now saying that Don't be afraid myself shows up if you pass the 6-dan doubles course. There's probably an easier way to do it, but nobody knows what it is yet. The "keep playing and it will eventually show up" method should also work here, so if you can't pass that course, just be patient and keep playing (it will probably take a while).