Electronic – Why GSM module connects with same apn for different operator

An antenna is essential if you want to connect to the network! If you look at the unit you will see a tiny coaxial socket marked GSM on the bottom edge, where the antenna needs to be attached. A similar connector marked GPS is on the upper left side, for a GPS antenna. Your Telit distributor should be able supply suitable antennae.

I have a very similar board that is on the photo you posted, but with SIM900A instead of SIM900.

You can't connect the RS232 Serial Port directly to Arduino because of mismatch in voltage. The voltage on these pins is higher than Arduino's 5V. You would need a TTL to RS232 converter to hook up Arduino to those pins.

This board has also another interface to communicate. Those 2 jumpers can be removed and then you have access to 2.8V serial pins. Looking at your photo - there are 6 of them, the bottom 2 are GND, and the top 2 are RX (the one on the left) and TX (the one on the right). The bad news is you also can't directly connect Arduino to these pins. You would need a logic level shifter to shift 5V to 2.8V. I've however used a bluetooth-to-serial module from ebay that outputs 3.3V and risked connecting it to these pins. It works smoothly.