Multiple people who weren't properly kicked from the game during maintenence claimed that the 'Summer Special' bundle was listed for 300 Lapis, providing a very good value. The Mythril Chest of Ability was said to be listed for $24.95 too. Not really worth it unless you just have to have that +10% attack or magic.
Believed to be a minor exploration event that JP had where you could run existing explorations as Vortex runs and fight an extra boss that dropped Screamroots and Star Quartz, as well as a guaranteed metal depending on the area (Copper, Iron, Silver, Mythril). Biggest detractor to this not being that event is that the sillouettes don't match the bosses that JPs had. Could be something unique.
A daily Vortex that drops gil turtles, metal cactuars, and magicites. I don't know exactly how it works, but I've always seen mention that it's pretty lucrative for JPs.
No idea on either of those. Maybe they're removing the Vortex of Trials and replacing it with both of those.