Single Mosfet driver to drive two N channel mosfet
Yes, you can control the two motors individually. Your schematic is missing a dot- generally you should avoid lines crossing as shown- offset one of the wires.

You could add a 10V regulator to reduce the gate drive to 10V but there is absolutely no reason to do so- the gates can handle 16V and 12V is better than 10V for reducing conduction losses. 

The series resistors on the gates are a good idea- they can help reduce ringing and overshoot/undershoot that could damage the gate driver and limit the current if it does occur.  

The bypass capacitor on the gate driver can be made large enough that the gate charge on the MOSFETs would not change the voltage much. A ceramic X7R cap in the 1uF range is usually good.