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.
Earlier on in the film, when the HEX Crystal is introduced, the guy doing the presentation says that the crystal will only detonate with that specific detonator and the detonator will only work with a particular frequency.
So A.R.I.I.A. is an incredible supercomputer that can process data from every wired surveillance source in the entire United States, can link together literally dozens or hundreds of seemingly irrelevant data points to produce conclusions... but can't decipher simple Morse Code?
She could, it just took the characters talking about it for her to figure it out. On top of that, she couldn't really DO anything to stop him.
So, why is it that when your massive government AI which can tap into everything threatens to kill off half the government, Jerry's brother doesn't do the smart thing and TELL SOMEBODY? He does DNA lock the computer so it can't control reaper drones(though apparently stops it from doing little else) but considering he works in the basement of the Pentagon, you'd think it would be really easy for him to go upstairs and tell his boss that "Hey, the giant AI in the basement just went Skynet on us. Maybe we should shut it down or something". You know, anything other then go home and get murdered before he can tell anyone. At least pass on a note to the guy who relieves at his post "AI planning to kill President.". Things the "most trusted enlisted person in the Air Force" is supposed to know how to do for his job.