Stack overflow is when you have used up all available stack space. The space available for the stack is, in most cases just an arbitrary limit chosen by the system designers. It is possible to alter this, but on modern systems, it's not really an issue - code that needs several megabytes of stack, unless the system is REALLY huge, is probably not correctly designed. 
The stack grows towards zero from "custom" - it has to go in a defined direction or it would be very hard to follow what is going on, and lower adddress is just as good as higher address. It used to be that stack and heap grew towards each other, which would allow code that uses a lot of stack and not so much heap to work in the same amount of memory as something that uses a smaller amount of stack and a larger amount of heap. But these days, there is typically enough memory (space) that the heap can be defined to be somewhere completely separate from the stack. Instead the stack overflow is detected by having a region of "reserved" memory just at the top of the stack that is not usable - so the OS gets a "trap" for using memory that isn't available, and the application can be killed.