yes, i believe wonderswan has a vertical orientation as well as horizontal
Yes, games were designed for you to physically rotate the console while playing.
Though for emulation that requires an extra button.
There are two sets of four action buttons (known as the X1-4 and Y1-4 buttons). They were arranged so that one set of buttons can be used as the D-pad, and the others as action buttons.
I think emulators usually requiring mapping buttons separately for each mode, but maybe some emulator is smart enough to auto-detect and remap them automatically.