Hi Angie,
Although the Hayabusa is technically available to use in March, I'm pretty sure all the seats have been booked up for the rest of the month. That said, there's no harm in asking at the JR ticket office when you activate your Japan Rail Pass! If there are no seats on the Hayabusa, the standard Hayate Shinkansen that goes from Tokyo to Aomori will be running as normal, and will take you up the country nearly as fast.
About Hiroshima, you can get the Shinkansen down to Hiroshima using an itinerary like this: http://goo.gl/4Rui4, so there's no need to worry about a slow train.
And as far as travel to Miyajima goes, you can use the Japan Rail Pass to get to Miyajimaguchi (26mins, route: http://goo.gl/YMVe4), where you can get the JR Ferry across to Miyajima island itself. The ferry to Miyajima is totally free for Japan Rail Pass holders!