What does 'z' in Z-transform represent ? Is it frequency or something else?
The Fourier transform doesn't exist for every signal. For example, there is not a Fourier Transform of the signal $ (2)^{n} u(n) $. So, in order to get an useful toll for this signals, you can multiply the signal for a sequence $ r^{-n} $ in order to make it decay fast enough to converge:

$$ X(\omega) = \sum_{n=-\infty}^{\infty}{[x(n)r^{-n}]e^{-j \omega n}} $$

$$ X(\omega) = \sum_{n=-\infty}^{\infty}{x(n)(re^{j \omega})^{-n}} $$

Then, we can make $ z = re^{j \omega} $. So, in this case, z is a complex value that can be understood as a complex frequency.

It is important to verify each values of $ r $ the sum above converges. These values are called the Region of Convergence (ROC) of the Z transform. The z transform is equal to the Fourier transform when $ r = 1 $, but the Fourier transform will only exist if $ r = 1 $ is inside the ROC.

As $ z $ is a complex variable, you can't plot it in a Cartesian graph as you said. You will need to plot an 3D graph where x-axis and y-axis contain the real and imaginary values of $ z $, and the z-axis the values of the z-transform. I don't know if there is a real utility for a graph like that in any application, and that's why it is not common to see this graph. Normally, the z-plane is enough.