lead-acid batteries have a normal voltage of 2.15 volts per cell, so a 6-cell battery will have a normal voltage of 12.9 volts. anything above 2.15 volts per cell (or above 12.9 volts for a 6-cell battery) will charge a lead acid battery. however most vehicle charging systems use a higher voltage for a higher charging reaction rate (the rate at which the battery gets fully charged). the optimum charging voltage is 2.45 volts per cell to achieve the highest capacity. for a 6-cell battery that means 14.7volts charging voltage. most vehicles have charging systems between 13.5-16.5 volts. as per my experience anything below 14 volts will not properly charge your battery, especially if most of your trips are short. more power is drained during starting than when the engine is running during those short hops, and the battery ends up dead.
if the voltage of your alternator drops below 12.9 volts then your battery is discharging. in other words it is supplying power to the load. this will drain the battery in the long run since the alternator is not charging the battery. remember it atkes 12.9 volts to reverse the chemical reaction in the battery.
as for your second question, the main purpose of the battery is to start your car. supplying electrical power to the electrical load when the engine is not running is only a secondary function. if your battery is dead, then your engine will not start.
I see, lets say at night, your voltage at night with aircon and full lights is at 12.3 volts at idle, but it goes up to 13v+ when revving-moving. is it enough to make your battery still at good shape?
there are some things to memorize when it comes to this .
well functioning charging system for 12v battery ;
A) * idle without load you should get around 14v
B) * idle everything's ON ( full load) you should get 13v - 13.5v
( below 13v is no good)
C) *2ooorpm without load , 14.8 v
* 2000rpm full load , 14v
12.3 v * IDLE , ( FULL LOAD) no good . check the wires , if wires ok , belt and battery are ok , that must be the alternator. you want to know the possible problems , anywhere from rectifier , stator, rotor or field coil, voltage regulator will cause this
to test the components;
FIELD COIL , no short to ground , 2-3 omhs
STATOR, no short to ground , continuity on all the leads ( it depends on the type of alt)
VR, can be tested by VR tester
RECTIFIER , half way rectification using a test light.
(light on both directions means the diode is shorted. no light on both directions = open diode) .