Hi can I ask for the square root (x^2), it is false because x supposed to be |x|, is that correct? But when we deal with simplification in algebra, do we need to do that or we can still treat square root of x^2 as x?

Yes

No, but it depends on the context. For instance, you *can* treat the square root of x^2 as x if you know that x is non-negative, for instance.