3 different ways to power the Mega2560 besides connecting to a PC:
7.5V to 12V 'wallwart' supplying DC to the barrel jack.
5V wallwart connected to the USB port.
5V wallwart connected to the 5V/Gnd pins on the Power header.
In the graphs they've got 2.5mA tops, so you've got about 2mV on that 1.2R shunt resistor.
And Uno's default ADC reference is 5V divided into 1024 steps each of them roughly 5mV. That's more than peak value of measured voltage.
And with such small sampling frequency you won't be even able to spot fast changes as you'll be measuring much slower that it ...
It seems, that the Sim800 module is drawing too much current, when you start it again. The voltage drops and the Arduino/Sim800 stops working.
This datasheet of the Sim800 states, that it can draw up to 2A when doing a sending burst. An USB port on a computer can provide up to 500mA and you can draw between 200mA to 1A from the Arduino's 5V pin (depending ...