For Army: Female enlisted offering CO. What does he want from her, in exchange for leave request approval ?

Without knowing the whole story, no, it is NOT normal. If the CO just happens to be a male and he wants her complete some important task that is part of her normal duties before he approves her leave, then I see nothing wrong with it. If on the other hand it is more personal in nature then she needs to discuss it with either the company EO rep. or the the battalion EO rep.

Is this a quid pro quo situation? If so, this type of situation is HIGHLY frowned upon and pretty much illegal.