For layered structures I recommend looking at this simple KB example of a 4-layer stack.
Regarding your questions, these are some comments and suggestions:
You need to choose the polarization of the source relative to the plane of incidence. The blue arrow in the source tells you the orientation of the E-field. In the 4-layer example mentioned above, the blue arrow of the source is pointing in the z direction, perpendicular to the plane of incidence (XY); this corresponds to TE polarized light. In the source settings you can see that the polarization angle is set to 90 degrees. If you change this angle to 0 degrees, then the E-field vector lies on the XY plane and so you have TM polarized light.
I am not sure I understand what you mean by unstable. Do you refer to the stability of the simulation for oblique incidence?
The wavelength can be chosen in the source settings > Frequency/Wavelength tab.
The choice of conformal mesh type depends on whether you have interfaces involving metals or PEC as explained here.
Since the structure is formed by thin layers, I would use a mesh override region for them so that you can control the number of mesh points inside the layers.
We have some useful getting started examples that take you step-by-step through the basic simulation settings; you might want to look at some of these examples. Also, we have some advanced metamaterial examples.