Question: 1. Are there any guarantees that C++ std IO will be portable across all Desktop and Mobile OS (I'm interested in iOS and Android)?
2. Is implementation of std IO different across the platforms or it is rather uniform? If it is different, then does it happen due to SDK of the platform (in other words - do SDK's provide those different implementations)?
3. Who provide those implementation? Who is the author? Does anybody update them?
4. Where is documentation?

Answer: 
Standard library is exactly that — standard. It's defined by standard. Every standard-compliant compiler must provide it. So the guarantee is that it will be portable across standard-compliant implementations (whether there's one for your target platform is a whole different question altogether). It has nothing to do with platform SDKs (whether it's implemented using one doesn't matter — the observable behaviour must be the same).
The idea of a standard (hence the std) is that it is respected and uniform no matter what platform you are on.
Some developers ship devices with support for all or some of the std library, it's really just up to them how it is implemented.

This is platform specific and probably available in each platform's SDK documentation, available most probably with the SDK or on the vendor's website.