Q1: The lateral earth pressure on a retaining wall

ANS:D - proportional to the internal friction of the soil

The Lateral earth pressure is directly proportional to the depth of soil because p=kwh.
The lateral earth pressure force is directly proportional to the square of the depth of soil
P(pressure force)= area of pressure diagram = 0.5kwh^2. Lateral earth pressure= k.w.h
(So directly proportional to h)

Lateral earth pressure force* = 0.5 k.w.h^2.

(It's force directly to h^2 but not pressure)

Here K depends on the angle of internal friction(θ) and retaining wall condition (active/at rest/passive).

For example At rest K = 1-sin θ.
Here lateral earth pressure and K decrease as the angle of internal friction θ increases. So lateral earth pressure is not directly proportional to the angle of internal friction. I think the answer given here is right,

See the problem here, asks about lateral pressure that is major stress and not active or passive earth pressure intensities. As per Bell's Formula on stresses,

P1 = P3* tan^2(α) + 2C*tan(α)

Hence here P1 i.e. Lateral Stress is directly proportional to the angle of internal friction.