CLT and Slutsky for power sums of i.i.d. variables

Let $X_1,X_2,\dots$ be a sequence of independent and identically distributed random variables with $E(X_1)=0$, $E(X_1^2)=1$, $E(X_1^3)=0$, $E(X_1^4)=3$. Let $S_n=\sum_{i=1}^nX_i$, $T_n=\sum_{i=1}^nX_i^2$, $U_n=\sum_{i=1}^nX_i^3$ and $V_n=\sum_{i=1}^nX_i^4$. Then, which of the following statements are true?