As the question states, is std::mutex fair? i.e., if thread A locked the mutex and then B and C call 'lock()' on it in this order, will they obtain the lock on the mutex in this same order or is the order unspecified?
The documentation doesn't address this at all.
The standard (§30.4) does not mention anything about requirements regarding fairness between contending threads on a mutex, so it might be or might not be fair.
In practice std::mutex implementations will probably use whatever mutex implementation their platform provides, which are moslty unfair, as this is usually simpler and more efficient. On windows e.g. mutexes are mostly fair, but not always. Some implementations e.g. Thread Building Block provide special mutexes that are fair, but these are not based on the OSes native mutexes, and are usually implemented as spin-locks (which have their own caveats).