Ok so now that I whaled for The New Arm-Chan I finally understand her abilities better
>She's not immune to paralysis specially, her sword can absorb electricity and shoot it and the more it absorbs the stronger she gets
>Her sword can also attack with ice but it can't absorb cold temperatures
>Most of her bullets are made of light according to the In game projectile types, but she also has some energy based attacks
>Her immunity to blindness is actually a gameplay representation of her main ability: the power to control her own history
>The Kasen of that universe can somehow control her own history and this Arm of hers comes from an alternative take on the origins of Ibaraki Douji
>Because of that Arm-Chan can selectively change her own origins to modify her abilities or avoid certain status effects.
There's a bunch of lore about her wielding Emperor's Jimmu's sword who's also a god and a bunch of other shit but the main point is that all that is alternate history Kasen gathered to create a new Arm