A. False, $\epsilon$ is common in both $(01)^*$ and $(10)^*$
B. False, LHS contain strings as $abab, ababab$ etc RHS doesn't.
C.True, $(p+q)^*p+(p+q)^*q+\epsilon =$ strings over $\{p,q\}$ those ends with $p$ $+$ those ends with $q$ $ +$ those doesnt end with p or q (i.e, $\epsilon$) = all strings over $\{p,q\}$ , i.e,$ (p+q)^* = (p^*q^*)^*$
D.False , all strings over $\{y,z\}$ (that also includes all strings ending with $yz$ ) $\bigcap$ all strings $\{y,z\}$ ending with $yz= (y+z)^*yz$