Which of the following statements are correct for instantaneous axis of rotation? 

In case of a wheel rolling on a horizontal plane, instantaneous axis of rotation of the wheel passes through A (point of contact of wheel with plane). But at A, acceleration is vertically upwards. It means, acceleration at A has non-zero value. Hence, option (1) is incorrect.

If the point is at a distance r from the instantaneous axis of rotation, then its velocity (relative to the axis) will be equal to $\mathrm{r\omega }$. But by definition, every point lying on the instantaneous axis of rotation is at rest at that instant. Therefore, the resultant velocity of the particle becomes equal to that relative velocity  $\mathrm{r\omega }$. Hence, option (2) is correct.

If distance of centre of mass of a body from the instantaneous axis of rotation is equal to r and if its moment of inertia parallel to instantaneous axis of rotation but passing through centre of mass is equal to ${\mathrm{I}}_0\text{, then }\mathrm{I}=\left({\mathrm{I}}_0+{\mathrm{mr}}^2\right)\text{. }$

Rotational KE of the body will be equal to ${\mathrm{I}}_0{\mathrm{\omega }}^2/2$ and translational KE of the body will be ${\mathrm{mv}}^2/2$, where $\mathrm{v}=\mathrm{r\omega }.$ Therefore, translational KE becomes equal to ${\mathrm{mr}}^2{\mathrm{\omega }}^2/2$. Hence, the total KE becomes equal to $\left({\mathrm{I}}_0{\mathrm{\omega }}^2/2\right)+\left({\mathrm{mr}}^2{\mathrm{\omega }}^2/2\right)={\mathrm{I\omega }}^2/2$. Hence, option (3) is correct.

In case of a wheel rotating on a plane, instantaneous axis of rotation of the wheel passes through A while the centre of mass is at distance R from A. In that case, the moment of inertia about instantaneous axis of rotation is equal to $\mathrm{I}=\left({\mathrm{I}}_0+{\mathrm{mR}}^2\right)$, where ${\mathrm{I}}_0$ is moment of inertia about the centroidal axis. Hence, moment of inertia of the wheel about the instantaneous axis of rotation is greater than the minimum possible value. Hence, option (4) is incorrect.