First of all, thank you for your willingness to help.
I believe I have flooded my posts with dispersed information which may have confused you at some point.
My intention is to replicate the exact behavior of a HM-10 module on a CC2541 circuit on a breadboard.
This is because the HM-10 module is too big for my purposes: I intend to use the BLE circuit in a smartband, so I need to have it as a SMD.
In order to do this, I have:
Flashed the CC Loader sketch available in this topic to an Arduino Uno.
Assembled the CC2541 chip the same way as demonstrated in this schematic.
Connected RESET_N (pin 20), DC (pin 34 or P2_2), DD (pin 35 or P2_1) to the Arduino Uno's digital pins 4, 5, 6, respectively. I have also powered the CC2541 with Arduino Uno's GND and 3.3V.
Flashed the firmware received from Hexor using CCLoader.exe with the command
CCLoader.exe COM_NUMBER firmware-file.bin 0
After these steps, I have successfully managed to make the CC2541 circuit execute AT commands! :D
Unlike the HM-10 module, however, the CC2541 circuit wasn't advertising (meaning I couldn't see the bluetooth module on my Android phone when searching for devices, not even with specific BLE apps).
If you have read my previous posts, I stated that I was using a mere wire as the Antenna, which was short-circuited between the pins 25 and 26, and also connected to the GND, which I believed was the reason why I couldn't see it from my phone. The Antenna wasn't exactly that which was specified in the schematic I provided.
Well, I saw on the schematic that the Antenna had a 50Ω resistance, so I also tried to replace the wire that connected pin 25 to pin 26 and pin 26 directly to GND with a resistor, and it made no difference.
Then I decided to make an antenna on a PCB following this reference (page 4), and connected one of the wires to pins 25 and 26 and the other to GND. Still, no difference. I'm starting to wonder if it's an Antenna issue or something else.