The circuit will work. Since the 10k is connected to VCC, it is not possible to drive a 12V motor with a 3.3V or 5V Arduino board.
A Schottky diode has leakage current with a reverse voltage. It depends on the temperature.
In a high frequency circuit, the 1N4007 is slow.
For example with a low energy signal of 100kHz, then the 1N4007 has capacitance and recovery time and will eat energy from the signal. The diode might get hot and the signal might be less strong.
However, as a flyback diode next to a motor, it is very fast. It can very easily take that pulse from the motor. That pulse from the motor is strong enough to overcome the capacitance and recovery time. With the low PWM frequency of the Arduino, it won't get hot at all.
I'm sorry that I don't know how to explain it better, I don't know all the details. In the past I also thought that the 1N4007 was slow.