The first real day of "Semana Santa" is Domingo de Ramos, the 20th. You will notice that many businesses will have abbreviated afternoon hours, as that is when processions begin their march. Everything will be closed on Thursday and Friday, which are national holidays, though for example there are always pharmacies that stay open, restaurants will also be open.
If you are dead set on doing the Seville Semana Santa, one possibility might be to stay somewhere in Dos Hermanas, though it can feel kind of far away from the action, it is the stop before Seville on the train line....and mroe likely to have rooms