Reading about RTOS, the characteristic of a "hard" RTOS is that it can keep a deadline deterministically but how do we test or prove that the system actually fulfils the requirements?
The MicroC/OS II RTOS is characterized as a hard RTOS but how can I validate that claim? If I have some C code and ISR for my FPGA that can run C programs and make context switch between threads with semaphores similar to what an RTOS does, how can I know whether the OS / RTOS is "hard" or "soft" RTOS?
Can it depend on the application and must it have a timer and therefore using the builtin hardware timer (e.g. the Altera DE2 has a 50 Mhz oscillator) with hardware interrupts is preferred, and then we just test whether threads and processes can be scheduled according to a deadline and we then check if the deadline was met?
Or is there some general practice to what must be included to make the difference between operating system, real-time operating system, and hard and soft RTOS?
Is there some "typical test" with a typical requirement for the label "hard RTOS" ?
It is hard to answer this question, because your premise is wrong.
A system classified as hard realtime is distinguished from a soft realtime system only through the severity of a missed deadline. In hard RT, a missed deadline is classified as a system failure, which may or may not cause harm to hardware and people, while soft realtime usually means that a missed deadline only degrades system performance, but does not bring it to a grinding halt.
A typical example for a hard RT system would be a watchdog that shuts down a system on overheating - if it fails to meet its deadline, the system breaks. Also, general safety-related systems in power plants, or airplanes fall in this category. A Soft RT example would be video streaming, where a missed deadline causes degraded visual quality or stuttering, but does not necessarily cause a failure of the system.
Long story short, hard and soft RT are characteristics of complete software systems, measured by their specifications and fault models. So typically, it is the application running on the operating system that fits the hard/soft RT criteria, the OS merely provides interfaces with predictable timing behaviour, that allow the application to make timing assumptions.