Answer
(a) stays the same
(b) III
Work Step by Step
(a) We know that the focal length of a spherical mirror is given as $f=\pm \frac{R}{2}$ and it does not depend on the medium. Thus, we conclude that the focal length stays the same even if the spherical mirror is immersed in water.
(b) We know that the best explanation is option (III) -- that is, the focal length stays the same because it depends on the fact that the angle of incidence is equal to the angle of reflection of a mirror. This is unaffected by the presence of the water.