is the XOR of PRG outputs a PRG?
This follows essentially from the security of the one-time pad: if you have some arbitrary distribution $D$ over a group $G$, and the uniform distribution $U$ over the same group $G$.  If $D$ and $U$ are independent, then sampling $x\gets D$, $y\gets U$ and computing $z=x\cdot y$, the resulting $z$ is distributed uniformly over $G$.

So, in fact, $G'$ doesn't even have to be $G(x_1)\oplus G(x_2)$; something like $B(x_1)\oplus G(x_2)$ for some arbitrary stretching function $B$ which doesn't necessarily have to be a PRG would be also fine.