(i) Yes, plane and convex mirrors can produce the real
image, if the rays incident on the plane or convex mirror are converging to a point behind the mirror. A plane or convex mirror can produce a real image, if object is virtual.
(ii) No, there is no contradiction because virtual image
formed by the spherical mirror acts as virtual object for eye lens. Our eye lens is convergent and it forms a real image of virtual object on retina.
(iii) As, the fisherman is in air, the rays of light travels from rarer to denser medium, so they bend towards the normal. Therefore, the fisherman appears taller.
(iv) Yes, the apparent depth decreases, further when water
tank is viewed obliquely as compared to the depth when seen normally.