To what requirements / assumptions RSAs & EMAS designed?
I will try to answer as much of this as I can, but there may be some holes to fill:


  Is RSA/EMAS designed for impact loading at the point of touchdown and to absorb energy of the moving aircraft for deceleration?


No, the arresting materials is only there for a runway overrun condition. It is not designed to absorb an aircraft impact, nor is it designed for an aircraft to touchdown on it, crash or normal landing. EMAS area's are very specifically marked:


(Source: BusinessInsider.com)

As you can see, the area is actually very small, and the markings denote that this is not a touchdown zone. It would be very hard for a commercial airliner to hit that small patch on touchdown, purposely or not.


  Assuming that the landing gear is down: Can the load be assumed to be distributed equally through all wheels?


Not always, because this depends on the loading of each aircraft gear. The load can be thought of as being distributed evenly probably at the same ratio as the weight on each gear, but only when all the gear are inside the EMAS area. This wouldn't be true, for example, as the aircraft enters the EMAS and the EMAS is acting only on the nose gear until the main gear exit the runway and into the EMAS.


  Are the brakes applied to assist deceleration over the EMAS?


YES! The pilot is going to be braking hard to try to stay out of the EMAS, it is unlikely that they would release the brakes as they enter the EMAS. Remember that EMAS is basically very weak concrete. The pilot is probably going to be using all available braking (wheels, aerodynamic, thrust reversers, etc) to get the aircraft to stop. Once they enter the EMAS they've destroyed the EMAS pad, and have done significant damage to the aircraft. 


  What happens in case of belly landing and when there are burst tyres?


If a belly landing made it all the way to the EMAS, which is unlikely, I doubt that the EMAS will have a significant effect on stopping the aircraft. The EMAS is specifically designed to grab onto things that dig into it. By the time the aircraft slides onto the EMAS, whatever is "hanging" under the aircraft has probably been broken away. I don't know of any case where EMAS encountered a belly landing aircraft (other than one's who have broke off the nose gear), but I'm guessing that the aircraft would slide right over it.

Burst tires on the other hand would probably not reduce the effectiveness of the EMAS since it will still be dragging through the gear. 


  Is there any other loading case?


Not that I know of. The system is designed to arrest aircraft overruns. Specifically this means a normal landing but unable to stop on the runway such as in ice, snow, or water. It is not designed as a crash safety system.


  What are the max design loads and velocities?


If you want to read the FAA's Advisory Circular on Engineered Materials for Arresting Systems (EMAS) for Aircraft Overruns it has quite a bit of information:


  The design
  (or critical) aircraft is defined as that aircraft using
  the associated runway that imposes the greatest
  demand upon the EMAS. This is usually, but not
  always, the heaviest/largest aircraft that regularly
  uses the runway. EMAS performance is dependent
  not only on aircraft weight, but landing gear
  configuration and tire pressure. In general, use the
  maximum take-off weight (MTOW) for the design
  aircraft. However, there may be instances where less
  than the MTOW will require a longer EMAS. All
  configurations should be considered in optimizing the
  EMAS design. To the extent practicable, however,
  the EMAS design should consider both the aircraft
  that imposes the greatest demand upon the EMAS
  and the range of aircraft expected to operate on the
  runway. 


FAA Advisory Circular AC150-5220 22b, 9.c

And this one:


  Entrance Speed. To the maximum extent
  possible, the EMAS must be designed to decelerate
  the design aircraft expected to use the runway at exit
  speeds of 70 knots without imposing loads that
  exceed the aircraft’s design limits, causing major
  structural damage to the aircraft or imposing
  excessive forces on its occupants. 


9.g from the FAA Circular, emphasis mine.