First of all,I didn't realise I was using new nexus charger (1.35A) and I thought it was the old charger (2.1A). So that cleared the doubts if my chargers were faulty.
I did few tests, asked my dad who is an Electrical Engineer and came to the following conclusions.
When I'm charging my phone/tablet ; say I'm using 1A, the power given would be around 850-900mA . The power be always less than rated.
If I'm using my phone and charging with same 1A charger, and the power used by my phone is 500mA, I would only see 350-400mA power given to battery as net because the power given would be subtracted from power being used.
Using a 2A charger would charge the battery more quicker, about 2x but it would reduce the life span of battery as well and may damage the device.
As more battery is being charged, more amounts of electrons would be present inside battery so the flow of current would start to decrease slowly . (So it would take more time to charge in the end.)
If charge power is less than usage of device, you would see discharge of device. In this case using a high power charger would charge the device but still it would damage the battery.
Basically, there is a safety factor of a device/battery. So if more current flows into it, lets say it can withstand 1.2 A and came with 1A charger. Using 1.3A or higher would damage the device/battery nonetheless.
I hope this helps and thank you for all your opinions and suggestions
And you're correct in that while the device is charging, some current is used for charging while surplus current, if available goes to the running device. Once the device's battery reaches a full charge, the full charger current is available to run the device. If the charger is capable of providing the current needed to serve the device's needs, life is good. Otherwise, the cycle begins again.
Generally speaking, so long as you're not flogging your device by taxing the CPU and or GPU, a 2 amp charger should be sufficient to run say, a music program and a nav program using the GPS. Plug an OTG cable in and start hanging peripherals off of the dongle and all bets are off.