Will I read battery voltage/charger voltage/intermediate voltage between 15V and 12V.
No. If the meter probes are placed across the battery, you will measure the sum of the battery voltage and the voltage across the internal equivalent series resistance (ESR).
$$
V_{meas}=V_{bat}+V_{ESR}
$$
How do we get the exact battery state during charging to show the battery percentage in case it has some display of battery percentage.
To remove the effect of the internal resistance, the charger must be disconnected. However the charging characteristics for the various battery types are well known so the state of charge can be estimated based on prior knowledge.
The prior knowledge allows the charger display to represent the percentage charge state. As batteries age the prior knowledge may become inaccurate. So without personal experimentation (and even with) "exact" is difficult to obtain. Settle for approximate.
I have seen mobile phones charging at 9V....what does that mean. does that mean when I measure the voltage on the charger and battery during charging it will give 9V.
I can't say for this particular case. Assuming the charger's voltmeter is accurate it is displaying the voltage including the ESR voltage. Having said that, they may compensate for the ESR.
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Most batteries have a high ESR when discharged, and an insignificant (??) one fully charged. So the effect of the ESR may be trivial when all is said and done. If you really want a precise measure then measurement over time of the charging voltage, the charging current and the open circuit voltage is required for full understanding. Voltage measurements do not necessarily indicate the amount of charge transferred to the battery. That can be measured by integrating the current.
Constant voltage charging is only used when the battery is fully charged to compensate for leakage over time. Constant current or current limited charging is always used when charging from discharged. So placing the meter probes across the battery will always indicate the voltage given by the equation above.