Infinite Dungeon Rewards

I was wondering what the rewards in the infinite dungeon are. If I remember correctly, all I have gotten are musical scores. Are there any grade boosters in there? And if not, is PvP the only way to get them?

Nope only musical scores and Golden eggs

Golden eggs come from the boss on every 10th floor starting at 9. In the future, there will be exclusive monsters in the Infinite Dungeon. 

Moved to FAQ section - please ask objective game questions there.

Will the infinite dungeon be available after an update? Or will it be blocked until the new missions are done?

It will always be available.