felixhokc
My understanding is that if you failed and reapply, you go straight to the stage that you left off from (i.e. in your case, you should go straight back into Stage 2 without having to redo the tests of first interview). That is, providing they accept your application this time.
I am not sure about rejection letters...this is my first application. I would think that 2 months is a pretty long wait - perhaps you might want to contact HR again to check your progress?
Best of luck.