Electrical – How to wake up SIM800 module from sleep, after entering sleep mode 2 (AT+CSCLK=2)

One problem I can see in your code is the following line:

while (mySerial.available() < 0) {

The available() method returns the number of characters available and will never be negative, so that means your AT command will never be transmitted, in fact your main code probably isn't starting up. Also you're not terminating the command with a carriage return so try the following code:

while (mySerial.available() == 0) {
  mySerial.println("AT");
  delay(2000);
}

Often when playing around with a new GSM module I find it more convenient to be able to type things from a PC to check operation, so maybe for a start you could use something like this to pass data through:

void loop() {
  if (mySerial.available() > 0)
    Serial.write(mySerial.read());
  if (Serial.available() > 0)
    mySerial.write(Serial.read());
}

I used a very similar board recently with a SIM900 loaded that didn't come with much in the way of documentation and while searching I found some Arduino boards are set for auto-baud and some are fixed at 19200, so using a baud rate of 19200 that should work either way might be your best starting point.

The "continuous transmission" requirement cannot be met with regular HTTP requests, you are expected to use every GSM slot, ignoring any higher-level protocols.

This test verifies that the emission spectra are within required parameters; this is done by moving a bandpass filter across the spectrum and writing down the power of the signal received. As moving this filter requires some time, the signal must be present for the entire duration -- interruptions could hide problems.

You are still required to follow the GSM framing and disable the amplifier between packets to verify that the sharp transitions at the packet boundaries do not translate to transmissions outside the allowed range.

The module is already approved as far as I know, so there is most likely a non-functional testing variant of the firmware that was used in that certification, so you'd have to ask the vendor for either a copy of that firmware, or a pre-flashed module that can be used for verification.