Nothing, but iPhones only load software signed by Apple (on the app store), so said alternative SDK would be useless as Apple won't sign software made with it (and regardless, they won't sign an alternative browser engine as a matter of policy regardless of which SDK with was made with).

Nothing, but you couldn't implement an alternative SDK using the public APIs, since, well, the public APIs are the current SDK.

Not sure what you mean exactly. Let's say someone comes along, and re-implements all same APIs from scratch as open source. They'll be public, right?

But as TD-Linux said, Apple simply will refuse to accept it anyway.

Right, but you can't implement a lot of the APIs without calling into private kernel functions.