Frau, I was just thinking the same thing yesterday. We don't know that he was beating her. BUT abuse is not necessarily beating. They were arguing a lot according to reports (there could have been some verbal abuse or mental abuse--and also physical because we know that so many victims never report it). And I agree with Eilonwy, a murder-suicide usually indicates that the murderer was abusing the victim. And no, I don't think just because you have a brain injury you can go and selectively kill your SO (not your mum and daughter in the house) and then later (not immediately) kill yourself.
Two things are for sure, he killed Kasandra and he had issues.