You actually don't have to die in the pit. Once you get to the platform, exit the stage, then re-enter. Then do it three more times. It is like the requirement in original MMX in Armadillo stage; the requirement is have 100% and have that location come into frame multiple times but on separate visits. In the case of this game, three times and then it'll appear on the 4th time. No need to die for this. Also, if you get through all of the game up to here without dying then it'll show up on the first time.
For the input, I've not been having too much issue, but I guess it depends on the controller you're using. Down+Right/Left+shoot, doing it in a quick fluid motion. Takes practice. But also, if it's unclear to everyone, you have to be at full health to use Hadouken, just like the original. The example Hadouken that fires after stepping out of the capsule fires off regardless, but you have to be full health to use it.