They make it very clear that the students may have brought personal items, and if you think they might help, you can take those items from the kids you kill.
There's no book on bomb-making lying around. That kid had a relative who was a revolutionary - and a big influence.
I think Beat's "this country is no damned good" speech is a reflection on his own motivations - an extrapolation of the "these good-for-nothing kids today" mentality that most educators posess.
The government's reasons are simply population control. Thinning the herd. In the book and the manga, the BR Contests happen pretty frequently. The movie doesn't answer some of these questions - I think - because the source material was widely known, and people could fill in the blanks.
I mean, a knowledge of how school works in Japan is something you need to understand just to measure the passage of time when watching the film. Otherwise, you might get the idea that Shuya's dad offs himself a short while before Shuya ends up in BR. The reality is that years go by.
To my mind, that the kids don't know that BR is a law, and a competition, and a cultural thing, is meant to be a comment on how little they care for whatever is going on in the world around them...and how much they are sheltered from it.
In high school, I dated a Japanese girl. Her spoken english was excellent, but her written English hurt her college entrance exams. There was INSANE PRESSURE on her to get into a good school - which is a deeply cultural thing (or was, as the mid-80's - early 90's salaryman thing has totally dried up, and they're facing harsh economic realities there now - Shuya's father is a representative for that situation). The pressure was so intense that, upon graduation, she was shipped back to Japan by her parents. She lived in a spartan little box of an apartment, and WAS NOT ALLOWED TO HAVE A TELEVISION.
She had to argue for A CAR.
The idea was that her parents forbade her to do or own ANTHING that might impede her studies.
So I wasn't allowed to visit, and the distance killed the thing.
She did write, mentioned being stressed as all hell...
The irony of this is, while she couldn't own a television, she ended up on television - in some 90210 knock-off as a best friend of one of the main characters.
Anyway - her parents wouldn't let her OUTSIDE, let alone back to the states. Listening to that stuff in such bright detail made the notion of a bunch of kids not knowing what was happening in their country or within their culture - POP Culture being the exception, of course - completely plausible.
Sure, the film is flawed - but I think that it's supposed to be more about cultural ideas and identity than the rules of the competition. The BR Island and its inhabitants are a microcosm in a petri-dish/pressure cooker. Kitano says life is a game, and the BR game's logic - such as it is - makes better sense than the logic of life. The Battle Royale's controlled chaos is somehow prefereble to the uncontrolled chaos of our world.
Then again, it could be argued that the BR's measured insanity only ADDS to the immeasurable craziness of a country and culture in desperate trouble - which is, to my knowledge, what BR2 touches on...
...while it sucks, sadly.