Is there any way to save the waterfall plot of gnuradio in image file or any other format?
Middle-mouse-button -> Save.
If not is there any other way to show the spectrum occupancy for certain amount of time in one image or graph?
This is a typical case for "offline processing and visualization". I'd recommend you just build a GNU Radio flow graph that takes the samples from the USRP, applies decimating band pass filters (best case: in shape of the GSM pulse shape), and then calculates the power of the resulting sample streams (complex_to_mag_squared) and then just saves these power vectors.
Then you could later easily visualize them with e.g. numpy/matplotlib, or whatever tool you prefer.
The problem really is that GSM spectrum access happens in the order of microseconds, and you want to observe for 24 hours – no visualization in this world can both represent accurately what's happening and still be compact. You will need to come up with some intelligent measure built atop of the pure occupancy information.