How can a wave be confined to a finite region of space? If light is a wave, then how can it be confined to a small region of space, and thereby turn into a photon?
Why doesn't light wave escape that region of space? If you splash some water in a pool, those waves cannot be contained by just water.
 A: 
If light is a wave, then how can it be confined to a small region of space,

Waves are modeled with periodic functions, sines and cosines, and the functions are solutions of wave equations. Their simplest form is the plane wave of a single frequency. 
The waves make wavepackets of several frequencies in a manner to appear at limited space time, 

This happens for water waves and sound waves and also classical electromagnetic light.

and thereby turn into a photon?

Photons are a different story. Classical light emerges from a superposition of zillions of photons, note, superposition, not addition, photons are not bricks but quantum mechanical entities. An individual photon in quantum electrodynamics can be described by a wavepacket , but it is a different story than classical lightwaves. Quantum mechanical waves are waves in probability distributions not energy.

Why doesn't light wave escape that region of space?

Light wave packets leave with velocity c. Think of morse signals with light.

If you splash some water in a pool, those waves cannot be contained by just water.

have you tried it?
