Apple allows, where "allows" means both "by the terms of service" and "exposes APIs to make that possible", apps that modify the way Safari works and the Safari web browser experience on the iPhone? (I'm asking, I honestly don't know).
No, you can build a new application using the engine that powers "Safari". This includes page rendering, and more importantly JavaScript execution. The latter is important simply because the terms of service only allow 3rd party code execution using Apple's "interpreter".
