"However, the plan is for that stage to vanish once one day has passed. It’s a once-in-a-lifetime encounter."
So, if its a really good stage, you can't keep it? Lame 
Yeah there's probably an option to save them if you like them.
This got me more excited than Sonic honestly. YES. Me and my friends will have tons of fun with this one. I know i'll be remodeling levels from old games (Metroid, Mario, Kid Icarus, etc) and forcing my friends to play as those characters for DOUBLE THE FUN.
Also how'll this work with picking stages in general for regular multiplayer matches? Will 'Random Stage' count towards custom stages as well?