How actually is the working mechanism of a red LED in Li-ion battery charger, it's turned on when no current (open) and when pretty high current (is charging), finally the current gets low when the battery at max volt and full charged causing the LED turned off and another LED, the green one, turns on ?

 

Hello,

The led is likely a status indicator of the charging chip used in the charger.
Without knowing wich chip is used, we can give you no details.
There can de two types of leds be used.
A two pin led with the red and green led anti-parallel in it or a 3 pin led with separate red and green leds in one package.
https://www.railwayscenics.com/3mm-20v-colour-red-green-led-resistor-required-p-994.html
https://www.railwayscenics.com/3mm-red-green-colour-common-anode-pin-diffused-22v-led-p-3271.html

Bertus