Few doubts

In Q1, the boy can see his full image.

Reason: For the boy to see a full image of himself, the mirror should be such that it is half his actual height.

Here the mirror is half his actual height, and is placed 0.8 m above ground level. So the mirror is 0.5 m above the boy's height. He can see his head.

The boy's eyes are 0.6 m above bottom of the mirror, so he can see a total range of 0.6 + 0.6 m till the bottom. Since his height from the ground till eyes is 1.4m, hence the boy can't see the bottom 0.2 m.
Hence he cannot see his feet.

For Q2, give me the frame of reference. Are you asking the velocity of image from an inertial frame of reference, or are you asking the velocity of the image with respect to the object?

If you are asking velocity of the image as viewed from environment (view it as per the image you have drawn), the rate of approach towards the mirror is the same as the rate of the object approaching the mirror. In this case, i am giving you SPEED of the image. So answer is 5 m/s.

If you are asking relative velocity of image w.r.t object, answer is 5√2 m/s.

No idea mate... i have to refer optics chapter.