Zero is a digit and thus it is a number. A number without value but nonetheless a number. Your thread demands a deeper understanding of mathematics that I cannot help you with.
You said:
By logic x+0=x, x/0=x, x*0=x and 0/0=0.
x + 0 = x...correct.
x/0 is undefined not x. We cannot divide by 0.
x • 0 = 0. Zero times anything is nothing.
0/0 is not 0. It is called an indeterminate form.
Search online for a history of zero and real numbers.