File IO libraries should be available via Linux headers, a secondary API as a custom, simplified interface should be reasonable; however, users need to be able to access system files, and anyways, they should be restricted by file permissions or processes that have locked said files during usage.
A BASIC interpreter would be a bit pointless, IMO; it teaches an outdated syntax with a limited range of modern practices and extensions (more advanced libraries, OOP, functional programming, different type systems, etc.), so I would instead suggest that a group of programming languages are available, all with interfaces to the custom distro's secondary API (that sits on top of Linux code). I would personally suggest Python, Perl, Lisp (or maybe Haskell?), C++, and all major Web scripting languages (HTML5, JS, CSS, PHP, etc. [since these don't require a compiler/interpreter, the associated software would probably be server hosting and a WYSIWYG editor]).
Granted, that's probably a bigger and more unreasonable task to ask for, but it's much more convenient and applicable.