Recall the defining equations of linear SHM

In linear SHM, the restoring force and acceleration are given by $F=-kx$ and $a=-\omega^2 x$ where $x$ is displacement from mean position.

Check statement (A): Restoring force is directly proportional to the displacement.

Since $F=-kx,$ the magnitude of restoring force is proportional to displacement, and the negative sign shows it acts toward the mean position.

So (A) is correct.

Check statement (B): The acceleration and displacement are opposite in direction.

From $a=-\omega^2 x,$ acceleration is always opposite to displacement.

So (B) is correct.

Check statement (C): The velocity is maximum at mean position.

In SHM, $v=\omega\sqrt{A^2-x^2}$ where $A$ is amplitude. This is maximum when $x=0$, i.e. at the mean position.

So (C) is correct.

Check statement (D): The acceleration is minimum at extreme points.

In SHM, $|a|=\omega^2 |x|$ so acceleration magnitude is maximum at the extreme points where $|x|=A$, and minimum at the mean position where $x=0$.

Therefore (D) is incorrect.

Select the correct option

Correct statements are (A), (B), and (C) only.

Hence the correct option is: $\boxed{\text{C}}$

Comparison with stored answer

Stored correct answer: C

Our derived answer also is C, so they agree.