Drawing an adjustable rectangle in Tikz

If you want to keep using your code, then this solution works.

Basically I renamed your command to something else, and put it inside of another newcommand that will add the boxes later, which you can customize by changing the border color or width.

I added a counter to your foreach commands and used those to rename your nodes as row-column for better reference. Then I used those to get the anchors needed for the boxes.

This solution assumes:

• that you will keep using 4 answers, i.e. A, B, C, D
• that you will keep using this format for the cheatsheet

So if you want further customisation, that's possible but I'd rather rebuild your code from scratch so that I'm sure it's robust and works for other use cases.

Note: If you change the number of questions, you need to compile twice!

Output

Code

documentclass{exam}
usepackage{tikz}
usepackage{multicol}

newcommandencircle[2][]{% 
    indenttikz[baseline=(nx-ny.base), remember picture]{
    node (nx-ny) [draw, shape=circle, inner sep=1pt, outer sep=10pt, #1] 
    {strut$#2$};
    }
}

ExplSyntaxOn

newcommand{createrows}[1]{%
            foreach x [count=nx] in {1,...,#1}  {%
            noindenthspace*{10mm}llap{textbf{x}}hspace{5mm}space
            foreach y [count=ny] in {1,2,3,4} {% 
                l_encircle {x}{y}  %
            }newlinenewline%
        }%
    }
cs_new_protected:Npn l_encircle #1#2 {    { encircle{int_to_Alph:n{#2}} }
}
ExplSyntaxOff

newcommandanswerspace[2][]{%
createrows{#2}%
begin{tikzpicture}[overlay, remember picture]
    pgfmathtruncatemacrohalfofrows{#2/2}
    pgfmathtruncatemacrosecondhalfofrows{#2/2+1}
    draw[line width=1pt,#1] (1-1.north west) rectangle (halfofrows-4.south east);
    draw[line width=1pt,#1] (secondhalfofrows-1.north west) rectangle (#2-4.south east);
end{tikzpicture}
}

begin{document}
begin{multicols}{2}
    centering
normalsize 
answerspace{24}
end{multicols}
end{document}