The notion that the frictional force in part b) is actually equal to the horizontal component of the pushing force is something that people get wrong often... rilla did it exactly right...

Checking that the pushing force (x-comp only) is less than the maximum static friction force tells us that it doesn't move, but that means the ACTUAL static frictional force is simply equal to the x-component of the pushing. People often will incorrectly answer that the static frictional force IS the maximum static frictional force. just thought i'd mention that in case you don't recognize the distinction in 'Rilla's solution.