if X1, X2 are independent, can we say X1^2 and X^2 or X1 and X2^2 are also independent ??
If $\displaystyle X_1$ and $\displaystyle X_2$ are independent, then for *any* function $\displaystyle f, g$, $\displaystyle f(X_1)$ is independent of $\displaystyle g(X_2)$. So the answer to your question is yes.
Sidenote: I put asterisk on *any* because actually not all functions work but you don't really have to worry about it.