Rust, as a language, has no allocator.

The standard library provides a global allocator. The collections in the standard library currently use that allocator.

It also provides an unstable interface for allocators in general. That's of course useful someday, but also doesn't prevent people from using whatever allocators they want in the meantime. It just means that libraries that want to be generic over one cannot currently agree. The standard library collections also will use that once it becomes stable.

No. There is a global allocator which is used by default, but all the stdlib functions that allocate memory have a version which allows you to pass in a custom allocator. These functions are still "unstable" though, so they can currently only be used with development builds of the compiler.