Very Hard Mode: Unlock upon Completing/Attempting Stages after finishing all four Arcs.
“Money is Power” Item: Appears to unlock upon finishing Flame Poem Arc, allowing you to spend QP to level up side story Servants up to the level of your highest Servant. The cost is level dependent with 3000 at lowest level and increasing by what appears to be 1200 per level.
Free Battle mode Stages are unlocked upon Clearing the Stage in Story or Side Story mode. The same boss can have multiple stages and multiple versions.