Using an Arduino, I guess I would modulate (PWM) the laser module and have the photocell light sensor pick up the frequency. Would this work?
Sure, photocells are slow in comparison to say an IR phototransistor. It depends what you are trying to do. For example, if you are trying to transport data to your arduino, I would use a phototransistor as you can get a higher data rate.
Depends on the applications or functionality you are trying to achieve.
I was thinking about making a little tank that has a laser "cannon" and a target (I want to be able to use the target in any indoor condition).
Either would work, in fact if you have a broken laser mouse - they have a very small camera which is very sensitive to 650 nm (pen/keychain laser) light.
If you have a red pen laser and a working laser mouse, you can do an experiment without tearing anything apart. Turn the mouse over and just aim the laser at the little lens. You can see the mouse on the computer move around !
I plan on buying a green laser module but I might just as well use a cheap keychain laser. I don't have a useless mouse though :(.