Is carbon a direct competitor to rust?
I'd guess that the intention of Carbon is to enable Googlers to write new code in a safer language than C++ while still maintaining compatibility with existing C++ code. So the language looks like a direct competitor to Rust if (and only if) you already depend on an existing and hard-to-rewrite C++ codebase.
Is there a way to interface carbon with rust?
I don't see any easy way to interface Carbon with Rust, though. The same blockers that make it a nightmare to interface C++ with Rust -- all the semantics leaked by templates/generics -- will be there between Carbon and Rust since Carbon has to align its semantics on C++ for compatibility.
Should I use rust or C++?
[] if you can use Rust or any other established programming language, you should. Carbon is for organizations and projects that heavily depend on C++; We believe that Rust is an excellent choice for writing software within the pure Rust ecosystem. Software written in Rust has properties that neither C++ nor Carbon have.