Forgive me if I have this wrong but I think there is much misunderstanding about the elements of the offence charged and what has to be proven. Without any legal gumpf, the charge is that:
1) OP intentionally or recklessly killed someone AND
2) that none of the available defences to this apply - e.g. putative self defence, insanity etc.
OP has admitted that he did #1. The state still has to prove this just in case, for example, if OP claims at the trial that his statements were made under duress. So, despite his admission, they still have to prove the elements of the offence - that he made the decision to pick up the gun, chose himself to fire it into a confined space with lethal/deadly ammo, and that his actions did or were very likely to kill the occupant in the toilet and they did in fact die as a direct result of this. They dont have to prove that he knew that they would die, just that it was very likely they would (reckless, called dolus eventualis). They also dont even have prove for #1 that OP knew who he was killing, or was likely to kill. In my opinion, little in reality was needed to prove #1 and I think this has been established - his gun, he fired it, the ballistics evidence, the injuries etc. I recall a remark by the judge when Nell requested adjournment before the public holiday, she said "she thought it was reasonable as the state had made a case". The defence has given no indication that him being the killer is disputed.
The most difficult part is #2, the putative self defence and that is what the case is about. The test is subjective, i.e. what OP felt/thought at the time and his fear of intruders, he thought it was an intruder etc. It is difficult to rebutt something in someones head. So all the state can do is to try to prove things like he knew it was Reeva and not a burglar as she screamed and if witnesses in the neighbourhood heard them he must have too, if he was so fearful of crime and had been a victim, how come he had never reported one before, that she was scared of him and they'd had problems, increasing the likelihood of an argument and rebutting the 'deeply in love' as well as generally discrediting his testimony by establishing he has lied and evidencing his general recklessness etc. etc.. They are doing this to prove that #2 - putative self defence doesn't apply, rather than prove #1 that he killed someone. So, this sort of evidence can't be considered for it's worth in proving he killed, it has to be considered re it's worth in establishing that his thoughts at the time were reasonable given his circumstances.
Hmm, I hope that makes some sense!