Hello, David,
I can't help with everything in this question, but I'll take you through the first major questions.
The primary product of this reaction is 1-methylcyclohexanol. We also form the MgBr2 salt, but I didn't try balancing the equation, after I realized we don't need it to answer the percent yield question, other than to note that we'll get one 1-methylcyclohexanol molecule for every one cyclohexanone molecule.
The structure of 1-methylcyclohexanol is the same cyclohexane ring contained in the cyclohexanone, but the C=O aldehyde group is replaced with an -OH alcohol group plus a -CH3 methyl group.
From the data provided, we have (0.95g/ml)(17ml) = 16.15g of cyclohexanone. At a molar mass of 98g/mole, we have 0.165 mole.
Using a similar calculation for the alcohol product (0.92g/ml)(11.3ml)(1mole/114g) = 0.091 moles of 1-methylcyclohexanol.
The moles of product should be equal to the moles of reactant for a 100% yield. The actual percent theoretical yield is thus ((0.091 moles actual)/(0.185 theoretical))*100% = 55.3%
I can't help with the mechanism question.
I hope this helps,
Bob