If you change the order of tracks in the list currently playing, this will affect the next track played. The next track played is always the one immediately following the currently playing track at the moment the switch between tracks occurs.
You can always locate the currently playing track by pressing the find playing button at the bottom of the tracks window. If the currently playing track has been deleted, then playing continues at the first track in the list. You cannot delete a playlist while it is playing.
Two pairs of buttons move between tracks. The inner pair advance to the next track or plays the previous track. The outer pair advance to the first track of the next album or go back to the first track of the previous album. The album buttons are fully effective only after an album shuffle or a sort on album or track.