What is the range between two towers and then range between two networks if they are near by means any problem will occur or not?
It depends on too many factors. That may be as close as hundret meters, or as far as 30 kilometers...
In bigger cities, many cell sites (they aren't always on towers) are usually spaced between 0.5 to 2 miles apart, while in rural areas they can be 4-10 miles apart or even more. In the wide open desert in east California, some sites have a range of 30 miles, while some of those in NYC barely make it out a quarter mile. The reason for this spacing is so that the network doesn't get overloaded. Cell sites can only hold so many calls at once. In an urban area many people are likely to be on their phone at the same time. Adding more towers increases capacity but reduces the coverage of each tower (or other sites on water tanks, buildings, billboards, etc). Another easy thing to use as a rough guide is the height of the antennas, taller sites may broadcast a bit further those those closer to the ground.
We can't say the exact range between towers. Here they are between some houndreds and 30KM... Depending on many factors...