Given a regular grammar $G$, $L(G) = \Sigma^*$ is decidable?
By the "iteration operation" you probably mean the Kleene closure of the language. In the case of the language is $\Sigma^*$ its Kleene closure is clearly equal itself. But you do not provide detailed explanation about how to use this fact to decide whether $L(G) = \Sigma^*$. However, you could solve the problem as following: 

Solution 1: Convert the regular grammar into the corresponding DFA and take the complement of the DFA. The complement of a DFA accepting all strings has not accept state. So you can decide by checking whether or not it has an accept state.

Solution 2:  Convert the regular grammar into the corresponding DFA and minimize it. If this DFA accepts $\Sigma^*$ then the minimal DFA has only one state which is the accept-state. So you can decide by checking if the minimal DFA has only one state which is accept-state .