I have an Arduino Mega ADK (ARM Version Google ADK 2012). So can I provide power through the jack directly from a 9V Battery of 500 to 750mA to the Arduino?
yes
How about 9V 200mA? through the jack
200ma will limit the number or types of extras you can connect. If you only want to flash a couple of LEDs, it will work.
Weedpharma
How about 9V 1500mA? Is it safe?
SagarDev:
How about 9V 1500mA? Is it safe?
Electrical devices only take as much current as they need - there's no problem with having a supply capable of providing more (other than size/weight/cost).