Just wondering if I could use two LM7805's in parallel to double the output current
No. Currents wont necessarily split evenly.
Related question: Is the heat dissipated dependent on current draw AND voltage reduced or just voltage reduced?
Both. Heat is related to power and power is calculated as Watts = Volts x Amps. (And in this case, it's the current through the regulator and voltage dropped across it.)
That's not the case with switching regulators because the voltage across the active component and the current don't happen at the same time. (Energy is stored in an inductor rather than being wasted.)