Welcome, duynq.mipt
The discretization of the computational domain into tetrahedrons.
Using a wave port, it calculates the power and "voltage" (by default) on a port. Then it calculates the difference in this quantity for the incident and total fields. You can get the exact equation in the help docs.
The curvilinear nature of the basis functions used to compute the fields in each tetrahedron. Study the FEM method to understand this further.
I usually stick with first order, but it depends on your field structure. For a TEM horn I'd stick with first.
Only discrete is to be trusted. If you don't mind some possible error in the behavior indicated by the S-parameters, then other types such as fast will do.