How is the phase of the stimulated emission in a laser first "chosen"? As I understand, once you have a population inversion and the excited atoms decay they will emit in random directions, and the ones that emit along the axis of the medium will cause stimulated emission.
Suppose an atom decays and starts the process of stimulated emission with some phase, what is preventing another atom from emitting spontaneously along the axis and causing stimulated emission but with another phase?
 A: A population inversion can only be achieved when the probability of spontaneous emission is small; so usually a single spontaneously emitted photon will give rise to stimulated emission and this sets up the laser action.
However, if two photons were by chance spontaneously emitted simultaneously, then two modes could start to form in the laser cavity - one corresponding to each "seed" photon. But when observed at the output of the laser, these two modes add up to a single mode with a specific phase which is the superposition of these two (assuming that the cavity is constructed so as to allow only a specific frequency / number of wavelengths along the length of the cavity).
Note that many spontaneous emissions will not be sufficiently along the axis of the laser cavity to result in amplification, and as such the scenario described is very unlikely. And finally, in many situations, one mode starts out being "stronger", will be amplified more, and will end up dominating - but in principle it is possible for two modes to exist simultaneously.
Very nice reference can be found at http://www.worldoflasers.com/laserprinciples.htm - worth reading up on the principles of lasers.
A: Your are not describing stimulated emission, but spontaneous emision. In such a case, when an electron is excited from a lower to a higher energy level, it will not stay that way forever. An electron in an excited state may decay to a lower energy state which is not occupied, according to a particular time constant characterizing that transition. When such an electron decays without external influence, emitting a photon, that is called "spontaneous emission". The phase associated with the photon that is emitted is random. A material with many atoms in such an excited state may thus result in radiation which is very spectrally limited (centered around one wavelength of light), but the individual photons would have no common phase relationship and would emanate in random directions. This is the mechanism of fluorescence and thermal emission.
Now, in a laser, you ave stimulated emission, the exited states are chosen because they have low rates of spontaneous emission (if there is any spontaneous emission, it will be low and do not be a sigbificant source of noise). The light generated by stimulated emission is very similar to the input signal in terms of wavelength, phase, and polarization. This gives laser light its characteristic coherence, and allows it to maintain the uniform polarization and often monochromaticity established by the optical cavity design 
