(i) A clear cloudless day-time sky is blue because molecules in the air scatter blue light from the sun more than they scatter red light. The phenomenon involved is scattering of light.
(ii) Atmospheric layers have different refractive indices of light. So, the light from the star is refracted in different directions. This causes the star's image to change slightly in brightness and position, hence "twinkle. The Phenomenon involved is refraction of light.