Does a transistor work by connecting the collector to emitter? If so, why do transistor regulators work?
Think about the base and emitter - to get current through the collector to the emitter, the base-emitter region must be forward biased. Given that the base has 5.6 volts on it, the base-emitter becomes naturally forward biased when the emitter is at 4.9 volts. This places the base 0.7 volts higher than the emitter.

If more current tries to pass from the collector to the emitter, the emitter voltage might start to rise and this would shut-off the base-emitter junction and reduces conduction. Hence this cannot happen.

This circuit is called an emitter follower i.e. the emitter has to follow the base voltage minus the 0.7 volts (or so) that is required to forward bias the base emitter region.


  And assuming the Vin (input voltage) is something like 10V, while the
  Zener voltage would still be something like 5.6V, why would the
  voltage at the emitter be (5.6V - 0.7V = 4.9V) and not 10V?


With 10 volts at the emitter (by some magical means) AND 5.6 volts at the base, the base-emitter region is completely "off" and thus no collector current can flow. In other words you paint an impossible scenario.