Does the formula \$Av\times \left( v_{in-}-v_{in+}\right) \$ of opamp applies also for DC voltage input?
Your formula only applies to an ideal op-amp.
For a real op-amp, you should consider an offset voltage term:
$$v_{out}=A_v\left(v_+ - v_- + v_{offs}\right)$$
This is true for both AC and DC inputs.
For modern commercial op-amps the offset term might be in the microvolts to millivolts range. For a very simple design like the one you're studying it is probably in the high end of this range or even many millivolts.
The offset effect is often compensated for by using negative feedback in the application circuit (or within the op-amp itself in more complex designs than yours).