My favourite character has to be Jasnah (Dalinar is a very close second). She's intelligent, witty, loves her family and has a thirst for knowledge; I love how Sanderson has created her and provided her with layers and an air of mystery (her book can't come fast enough for me).
As for scenes, it's almost too many to choose from! An instant favourite of course is when Bridge 4 saves the Kholins, as others have said I got chills all over. Another great scene is Shallan and Jasnah talking about the Parshmen in relation to voidbringers... the tension was fantastic and I could feel both of their horror at the realization of how dangerous a position they could be in in the near future.