Is it possible to connect a long rope (excluding the danger of it's breaking) to a geostationary space station and use it to transport food and other necessary item's to the station and then delivering it to international space station or any other place where it is required?
No, this is not possible because the weight of any rope that is the necessary 35 600 km long would very quickly pull the station out of orbit. Furthermore, since the station is effectively weightless in orbit, the act of hoisting something with weight up from the surface would create a reaction force on the station that would again pull it down long before the package left the surface.
Now suppose you countered these by using boosters on the station to keep it in orbit. The amount of fuel and energy you would require to use to achieve this would be equal to or greater than the amount of fuel and energy you require to use a rocket to blast it into geostationary orbit anyway