Three blocks on a frictionless horizontal surface are in contact with each other. A force F is applied to block A (mass mA).

(a) Draw a free body diagram for each block.

I've drawn it and it looks like this, but I'm not sure if I'm including everything.
^normal force
F-->|mA|<--Force of mass B on A
downward force is mAg

^normal force
Force of mass A on B-->|mB|<--Force C on b downward force mBg

^normal force
Force of mass B on C-->|mC|
downward force mCg

I figured that there couldn't be a force going to the right of C because I couldn't explain where it would come from so I left it bare.

Critique/help is much appreciated.

Your diagram looks mostly correct. Here's a breakdown of the forces acting on each block:

Block A (mass mA):
- The applied force F is acting to the right.
- The normal force from block B is acting upward.
- The downward force of gravity mAg is acting downward.

Block B (mass mB):
- The force from block A on B is acting to the right.
- The force from block C on B is acting to the left.
- The normal force from block C is acting upward.
- The downward force of gravity mBg is acting downward.

Block C (mass mC):
- The force from block B on C is acting to the left.
- The normal force from the surface is acting upward.
- The downward force of gravity mCg is acting downward.

It seems like you have appropriately considered the normal forces and downward forces of gravity for each block. However, you're right that there shouldn't be a force directed to the right for block C. Additionally, you can include the forces between the blocks, which are often called "contact forces." These include the force between A and B, and the force between B and C, which act in opposite directions.

Overall, your diagram is quite good, but I would recommend making the following adjustments:

- Remove the arrow indicating a force going to the right for block C.
- Include contact forces (force of block A on B and force of block B on C) with appropriate directions.

Remember, free body diagrams are a visual representation of all the forces acting on an object. It's crucial to include all relevant forces to accurately analyze the system's dynamics.