The correct answers are Any magical broom will fly if you just believe! and I have some spare invisibility cloaks in the closet.

Any can actually be used in affirmative sentences when it means "it doesn't matter which one" (like any magical broom).

"I need any sleep" is incorrect because for standard affirmative statements, we use some ("I need some sleep"). "We do not have some toad eyes" is incorrect because negative sentences require any ("We do not have any toad eyes").