Answer
See details below.
Work Step by Step
Since $\lim\limits_{x \to 0}x^2=\lim\limits_{x \to 0}-x^4=0$, then by the Squeeze Theorem, we have
$$\lim\limits_{x \to 0}f(x)=0.$$
No, we do not have enough information because in this case the conditions of the Squeeze Theorem are not satisfied. For example, you can see that $\lim\limits_{x \to 1/2}x^2\neq \lim\limits_{x \to 1/2} -x^4$.
