She'll use her broom to draw out several minutes worth of memory and the other 'cleaning skill' she got was she'll be able to sweep low level small monsters away.
The sword will get two skills so far. First one is called Slime Bringer that let Nagi summon slimes that are in the area. Second one is Self Regeneration, it allows restoring the blade to its former state in one hour, no matter how chipped or broken it is.
Nagi picked up Delay Arts skill from the sword. Basically once the skill is activated it decreases the offensive power to zero no matter how many times he swings the sword. Then when he's ready he chants unleashed and all that stored up offensive power is released in the next strike with it.