Apply Snells law for refraction.
Snell's law states that the product of refractive index and the sine of the angle to the normal is conserved across a boundary. Solving for the refracted angle predicts where a ray goes on entering a new medium. When light travels from dense to less dense, the required sine can exceed one — physically impossible — and the light is totally internally reflected instead, which is the effect that makes optical fibres and prism binoculars work.
Snell's law of refraction
n1 sin(theta1) = n2 sin(theta2), so theta2 = arcsin(n1 sin(theta1) / n2); critical angle = arcsin(n2 / n1) when n1 > n2
Because the normal is the only direction with a consistent geometric meaning at a curved or tilted surface. Measuring from the surface itself would make the law a cosine relation and would break down for non-planar interfaces.
Only going from a higher to a lower refractive index, and only beyond the critical angle. Water to air has a critical angle of 48.8 degrees, which is why a swimmer looking up sees the whole sky compressed into a circular window overhead.
Yes. Partial reflection always occurs at an interface, with the fraction given by the Fresnel equations — about 4 percent at normal incidence on glass, rising steeply as the angle grows.