Is the square root of $4$ only $+2$? Why is $4^{1/2}=+2$? 
It should also be $-2$ since both squared just give two only. Also why do we always represent root of $x$ on the right side of the number line? 

It is by convention: with real numbers, we agree to take the positive square root. This allows us to define $$f(x) = \sqrt x, \;\;x \in \mathbb R, \;\;x\geq 0, $$ so it is a true real-valued function: taking a square-root of a number greater than or equal to zero "returns" a unique real number (is hence a function). Without that convention $\sqrt x$ would fail to be be a function.
(Note: as imranfat suggests: I think you might be confusing the square root function with what we know about solving an equation $x^2 = 4$, which has two solutions, $x = \pm 2$. 
