I am not sure why I persist with this but here goes (please correct me, anyone, if I am mistaken about any of this):
He admitted killing her-- no further evidence needed for that. The determination of murder (DE) is up to the courts. To convict him of Dolus eventualis they need only determine if he foresaw the possibility of unlawfully killing whoever was behind the door. This is a subjective test, but as we have said many times this morning, the court is allowed to make reasonable inferences about the accused's intentions.
The killing is considered fundamentally unlawful because Pistorius was mistaken about being under attack and therefore it does not meet the criteria for what would have been a lawful killing in self-defense.
According to some legal scholars, Masipa erred in her application of PPD in Oscar's case. Apparently key aspects of his PPD claim do not meet the legal standards necessary to justify his response to the perceived threat, including an excessive use of force against an unknown target when he had other options. If Masipa is found to have erred in her application of PPD in Oscar's case, then he will be considered eligible for DE.
The appeal will also revisit whether the court should have made the reasonable inference that a trained and licensed firearm owner would have the foresight to know that firing four rounds into a small toilet cubicle would likely kill the person behind the door.