benzophenone + NH3OHCl --> benzophenone oxime (+acid) ---> beckmann rearrangement --> benzanilide

Benzophenone is partially soluble in hexane. Benzophenone is polar, where as, hexane is nonpolar. "Like dissolves like."

From least to most polar: biphenyl >> benzophenone >> benzhydrol

The question here is asked in a slightly incorrect manner. Assuming I understand exactly what you meant to ask which is "In a reduction of Benzophenone is Diphenylmethanol created with a 1/1 molar ratio?" then the answer is yes they are. For every mole of benzophenone one mole of diphenylmethanol is created.

Benzophenone is a reagent and diphenylmethanol is a product in a reduction of benzophenone reaction. However if you're referring to a reaction which creates BOTH diphenylmethanol and benzophenone as products, then you would need to provide the reagents that create the two.

The carbonyl group of the benzophenone acts as a hydrogen bond acceptor with the alcohol group of methanol.