The U.FL should be on the same layer of the MC60?
Yes, it is better to have an antenna connector (U.FL or any other) on the same PCB layer in which high-frequency RF signal is being generated or being received. The routing of high-frequency signal traces between different layers is generally not advised in view of impedance considerations (as vias tend to introduce impedance mismatch).
Also, try to keep the length of the antenna trace on PCB as small as possible. This will help in reducing coupling of any noise (electrostatic/magnetic) due to other components and traces present on the same PCB.
Also, it should be far from the SIM card holder and power source?
Try keeping it far from sim card slot and it's PCB traces as they seem to be interfering with each other. You can also try shielding SD card PCB traces with a grounded metallic cap. First see if it starts functioning properly with the antenna by considerably lowering the transmit power (if it does, that means interference from the transmit signal is most probably the issue).
In the datasheet of the MC60 they don't say anything about a internal RF antenna, how is this possible?
Any material in which EM waves are capable of generating electron oscillations will act as antenna. Thus any piece of metal will act as antenna (although a bad antenna). How good an antenna it depends on its shape, dimensions, structure. So a properly designed antenna (e.g. the one which you are connecting to U.FL connector) will have good antenna parameters like low return loss, low VSWR, proper radiation pattern, gain etc.
In your case, the copper trace which is flowing from IC package to U.FL connector seems to be acting as an antenna. And it also seems that you are quite close to the telecom tower. You would see that if you get it working with a proper antenna the range over which it would communicate with the tower would be way better than the case when there is no antenna connected to the U.FL connector.
The entire MC60 module is enclosed with a metallic cap. This cap shields the internal components from any kind of external EMI noise. An internal antenna under such cap won't function properly as any RF signal to it or from it would get blocked by the metallic cap.