How to design a PCB to connect the GSM modem with 50Ohm track impedance?
The electrical length is the phase shift that the design frequency experiences when travelling down the trace.  In this case, it is irrelevant.  For some designs, these delays must be known adjusted to specific values.  Quarter wave transmission lines of specific impedances can be used for impedance matching and in the construction of various RF components.  For this, you need an electrical length of 90 degrees.  In your case, the length is irrelevant.  For the ground vias - just position them in some what that they don't interfere with the impedance controlled trace.  The signal via probably won't be very close, but at 1800 MHz, it's too small relative to the wavelength to be much of a problem.  I wouldn't worry about the connector too much either for the same reason.  At 2 GHz, the wavelength is about 15 cm.  If any 'discontinuities' are less than 1 cm (1/16 wavelength), you should be fine.