Struggling to get my SIM800c blinks the LED

I have a SIM800c module with the following sequence of pins:
Top side: 5v, V_TTL, GND, TXD, RXD, DTR, SPKP, SPKN
Bottom side: MICN, MICP, Ri, VRTC, GND, PWR, GND, VBAT
The vendor told me that the module already comes with an internal antena, but it also has a connector for another external one. So I decided do not purchase the extra antena, and now I wondering if this can affect the behaviour of SIM800c.
The module is being powered from an external 12V power supply connected to a step down module lm2596 adjusted to give the 4V required by SIM800c. I also use the capacitors and the zener diode as recommended in the module datasheet. The power supply is connected to the 5V pin, and when I turn on the circuit a red LED light up indicating the the power is on, but no blinking LED appears on the module.
Before trying things that can damage my module, I would be very happy if someone could help me to answer the following questions:

  1. Can I power the module with 5v through the 5v pin, instead of 4v? I want to trying this because I’m getting around 2,74 in the VBAT pin, when I power the module with 4v. I also ask to myself why there is a 5v pin in the module since the maximum voltage recomended to SIM800c is 4.4v.
  2. Can I power the module through the VBAT pin, using the same power supply or a 9v Ni-Mg battery + step down, instead of the Li battery recommended in the datasheet?
  3. Should I use an external antena as well?
    Thanks in advance.

A picture would have been helpful. If your board is designed to run at higher voltage, you should use the same. If you want to directly run at 4V then give it directly to modules VBAT pins. Get 4V points on VBAT first and then pull the PWRKEY pin down to boot the module and LED will blink after it boots

Thanks for your help! I had some progress with the setup I’m currently using, as showed in the link bellow
https://1drv.ms/u/s!AinrKH6TYflctA2BybWzh4nrM-qM?e=ZW6fNX
I feed the module throught the VBAT pin with 3.8V, instead of 4V. After pressing the button during at about 1s, the LED blinks at every 1s, and soon starts blinking at every 3s.
The problem now is that the module doesn’t respond to AT commands (serial1.available() returns zero), and nothing is printed in the arduino terminal.
If I try using the 5V pin instead VBAT, the module doesn’t work at all - only the POWER LED lits.
I don’t know if in SIM800C we can directly connect its Rx pin to Arduino’s digital pin, since Arduino Mega uses 5V GPIO and maybe the module is NOT 5V tolerant.
It’s hard finding clear information on internet about this issue in SIM800C, so I’m still stucked on it, and your help is very important to me.
Thanks for your atention.