getting arduino PWM from 0-5V to 0-10V or 0-12V?
Is there a solution that make pwm go up to 0-12V?

Yes, you can use level shifters in this case
What effects on the driver if I reduce VCC to 12V?

What I get from data sheet is it will increase the Turn OFF Delay, Turn ON Delay, Shutdown Time.
Is there formula for capacitors other than the bootstrap one and what their purpose?

What do you mean by this?