What is the white precipitate that forms when benzophenone is added to your grignard solution?

Phenols have a general acidic character and they react with Grignard solutions similarly to how water would react. The product is that the Mg group of the Grignard reaction is replaced with a H (that is easily available due to the acidity of phenols) and we have that Mg(OH)X is created. The grignard solution is: R-Mg-X. This metal hydroxide creates a white solid compound that is not soluble in ether and it is what you should see after adding phenol to the solution.

Nonmetals usually react by gaining electrons

They can measure  the amount of energy gained or lost