Let $L(R)$ be the language represented by regular expression $R$. Let $L(G)$ be the language generated by a context free grammar $G$. Let $L(M)$ be the language accepted by a Turing machine $M$. Which of the following decision problems are undecidable? I. Given a regular expression $R$ and a string $w$, is $w \in L(R)$? II. Given a context-free grammar $G$, is $L(G) = \emptyset$? III. Given a context-free grammar $G$, is $L(G) = \Sigma^*$ for some alphabet $\Sigma$? IV. Given a Turing machine $M$ and a string $w$, is $w \in L(M)$?

Let us analyze each decision problem:

1. Problem I: *Membership problem for Regular Languages* (Given $R$ and $w$, is $w \in L(R)$?). Regular languages are decidable for membership. We can convert the regular expression to a DFA and check if it accepts $w$. Hence, this problem is decidable.

2. Problem II: *Emptiness problem for Context-Free Grammars* (Given $G$, is $L(G) = \emptyset$?). We can determine whether the start symbol can derive any terminal string by identifying all generating non-terminals. Hence, this problem is decidable.

3. Problem III: *Totality/Universality problem for Context-Free Grammars* (Given $G$, is $L(G) = \Sigma^*$?). The universality problem for CFGs is well-known to be undecidable (reduced from the Post Correspondence Problem or valid computation histories of Turing machines).

4. Problem IV: *Membership problem for Turing Machines / Halting problem* (Given $M$ and $w$, is $w \in L(M)$?). This is the acceptance problem $A_{TM}$, which is famously undecidable.

Therefore, problems III and IV are undecidable, which corresponds to option (D).