lemme try on the push-start/battery thing:
the batt is charged by the alternator ("magneto" + "coil" or
whatever they call it), which is connected on the crank. AC current
is converted to DC to charge the battery and power the CDI.
if your bike is the kick-start type, each action you kick is
actually charging that battery for that tiny bit and powering the
CDI for generating that spark. once your engine kicks into life,
it's a self-sustaining process. however, to ensure that your other
stuff like lights and indicators can work, a battery is needed to
power it. why? because the power generated by the alternator is
dependent on the engine rev. the purpose of the batt is to store
extra current when the alternator produces more electricity than
the bike requires, and this is used when you turn on the lights
etc.
electric start uses a starter motor to start. so if your batt goes
completely flat, you're screwed. if you press the starter and
nothing happens, could be that either the battery is flat or the
starter motor is screwed. test out the battery first. if the
battery is fine (lights etc), can still push start and head for
your mechanic to service the starter motor (or starter carbon or
electricals).
hope this helps! 
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rock hard... ride free...
