I am glad that you finally got some reasonable result.
It is the display that shows you the whole mode profile with symmetry-type of BCs.
Since you have used symetrical/symmetrical BCs the mode has such behavior. Please make sure that this is the mode property you desired.
FDE is to solve the mode profile for a waveguide cross section, which is usually 2D while the waveguide is 3D, and the 3rd dimension is infinitely long.
FDTD, on the other hand, can simulate actual 3D cavity. To find desired 3D modes, you can use specific symmetry BCs, proper dipole clouds and monitor groups. Since it is time-domain method, what you find is the resonant modes/frequencies, which may not show you the desired frequency (it depends on the mesh accuracy). The resonant frequency is the simulated result, not the pre-specified value. You can limit the excitation/analysis bandwidth. This will be another topic. If you have questions, please write a new post.