Why did Air France flight 447 fail to recover from the stall?
I‘ll attempt a very brief answer based on the report against your questions:

1) Why did the aircraft stall?
The aircraft stalled because crew pitched the aircraft up beyond the performance limit at that altitude (they pitched into a climb which the available engine thrust could not sustain, bleeding off speed until the aircraft stalled).

2) Why was power not reduced?
I don’t know, but in my view that didn’t play a crucial role, either.

3) Why did the aircraft not pitch down by itself?
Because crew didn’t realise they were stalled and continued to apply „nose-up“ control input. Seemingly inconsistent behaviour of the stall warning system and unexpected parameters on their instruments (i.e. a combination of speed and vertical speed not ever seen in normal flight) contributed to the situation.