I watch the behavior of the radio communication, if any unexpected behavior then I read my code 5 times over again.
Can you see radio waves? I certainly can't. So, I don't know what this statement means.
The FTDI cable is connected to the Arduino in one way, to enable the PC to communicate with the Arduino via a serial port. You can, after uploading code, open the Serial Monitor, and see anything that the Arduino uses Serial.print(), Serial.println(), or Serial.write() to send to the serial port.
I don't know if this Arduino can measure battery voltage.
Sure it can. Connect a the positive side to an analog pin, and the negative side to ground, if the battery voltage is 5V or less. If it is greater than 5V, use a voltage divider (+ to one end, middle to analog pin, other end to ground).
Sorry, but I don't understand your 'abuse' question?
You are trying to beat a battery to death, making it do various things, measuring how long those various things take to kill the battery. That's what I meant by abuse.
It still isn't clear whether the battery will be powering the Arduino, too, so that the Arduino stops sending data when the battery voltage drops too low. If so, then you are missing a great opportunity to measure and plot how the voltage drops off, if all you are sending for data is "I'm still here" every so often.