1 Sounds like either a non legit version or a version from another country that may not work in the UK. Or it needs downloads (see below)
2 the story mode game disc is effectively just a token/license to allow you to download and play the levels (episodes) – there are four at the moment with a fifth due before too long. The first episode or part of it can be played as a demo.
If his xbox isn’t connected to the Web and doesn’t have a MS live account (and I disagree that it’s geared to having to pay – nem jnr has an xbox and hasn’t paid for anything other than one minecraft skin (a couple of quid) in two years)) then he won’t be able to download the story mode levels.
Aside from that, you can’t get updates, bug fixes, etc if the console isn’t online. Parental controls are good so long as they’re set up so I’d suggest getting on and doing that and then sorting out getting it online.
It’s worth noting that getting the console online doesn’t mean he can play online, they’re two separate things – nem jnr doesn’t pay any online games on his xbox 360 (though he does on his pc – under supervision).
Happy to offer more advice as necessary.