Laser Receiver - What is the Time Response?

That means there is some way to speed the Rise time of this component, for example? Reducing 7us to Something faster?

Yes, reverse bias it. Also note that the quoted 7 us is with a 1K resistor load, so it would be 0.7 us with a 100 Ohm load. You probably don't need a 1 cm x 1 cm area, either.

But even 7 us rise time should be more than fast enough for your application, especially if you are using a 16 MHz Arduino.