Thank you all for the kind responses and alternative viewpoints.
I think in the end, (whether or not NZ police get round to releasing the autopsy/postmortem results), we may find out that she had probably been drinking, (anywhere from tipsy to drunk), and made a decision to go with that guy to his room, which she might not had done if sober.
He certainly probably tricked her into doing so, (which would have been easier for him whilst she was under the influence). Once they were both in the room together he probably came on to her straight away, she then rejected his advances, and that's when things may have got heated.
I'm thinking that either he forced himself on her and then killed her afterwards to cover his tracks or she resisted him and he killed her. He may also have harmed her to stop her from leaving his room. One thing is almost certain:- it was probably sexually motivated.
It is possible that residents near to his apartment room could have been alerted to Grace's screaming or the violence that was going on in the room, so he probably killed her with force very quickly. I'm thinking probably suffocation, strangulation or drowning as these methods keep the noise to a minimum and keep the victim silent.
It also keeps the body "intact". The forensics collected in the room could be anything from Grace's fingerprints, clothing, hair, skin, saliva or blood. If she was in the room they will certainly have found a treasure trove of evidence. With the body, car and shovel now found as well it seems certain now he will be convicted on all charges.
I think the shovel found played a role in possibly burying Grace where she was found, a few days after she had died. I strongly believe that Grace Millane died on Saturday night soon after going to his room. I doubt the suspect wanted to wait long with a pretty 22 year old in his room with only him.
Here we likely have a delusional young man with sexual fustration. I very much doubt she was the first that had rejected him, and since he had also probably been drinking with Grace had spun into a rage. In previous reports I read, previous house mates did say he was aggressive when drunk and did drink regularly, so that does make sense.