If you use Oath of Purging while in the Monastery, does it break immediately?No.
If an effect changes your default secrecy/grace, does your current value increase by that amount as well? or just the max?No.
Default grace is not a maximum. Your default grace only matters when something specifically refers to it; for example, praying lets you gain grace "up to default". Things that aren't specifically limited (e.g. a forgotten shrine) can take you above your default.
If changes to your default grace also changed your current grace, then you'd lose grace when a Corruption blight disabled your Holy Mantle and gain it back again when you destroyed the blight or left the area--I, for one, think that would be confusing and annoying.