1. Only the waveport is applied to a conducting medium - and it is actually a 2D EM solver on its own, trying to find the modes of the applied structures. Remember that even on perfectly conducting materials only the tangential (ie parallel to the surface) E-field components have to be zero (and the other way around for the H-fields).
2. HFSS is a frequency domain solver. So... actually yes, the excitation voltages, currents etc. are sinusoidal... HFSS V13 can also treat transient stuff. So I think, with V13 pulsed signals should be possible with that version.