Why would the first step to A.R.I.I.A.'s plan to have the characters blow up congress be to have them declared terrorists? It makes it kind of hard for them to get in.
Well, Jerry is supposed to be dead, and the authorities were not supposed to find out Rachel's identity. They only found out who she was through sheer luck.
Because that's what A.R.I.I.A. would do under normal circumstances. She doesn't want to behave out of character lest the people working in Eagle Eye shut her down for a diagnostic.
The entire plan hinged on the girl hitting a high note to trigger the bomb? What if she didn't, for some reason (which is extremely likely). Why not just use a conventional detonator?
My guess is that because of all the security a normal detonator would be detected. In addition that particular instrument that was meant to trigger the bomb was rigged to ensure she would succeed, during the film we see it altered just for that purpose.