CFG of all regular expressions over a binary alphabet
You are quite close to the solution. We will use a few variables, each corresponding (intuitively) to some other &quot;thing&quot;. Specifically, we will use the variables $S,E,A,B$.
$S$ is the starting variable. $E$ is a variable that will produce a valid regular expression (its called $E$ as short for &quot;expression&quot;). $A$ will be some valid string over the alphabet $\{0, 1\}$, and $B$ will be a non-empty string over that same alphabet.
The CFG will now be:
$S\rightarrow E$
$E \rightarrow (E)(E) \space | \space E+E \space|\space E^* \space | \space (E) \space|\space A$
$A\rightarrow B\space |\space e$
$B \rightarrow 0B \space | \space 1B \space | \space 0 \space | \space 1$
I hope this CFG is what you are looking for! (I don't know if it is, since you didn't state the definition of the syntax of a regular expression using this alphabet, so I have only tried to go by the examples)