Pure speculation on my part here, but I think a fairly likely scenario is developing based on Reeves having dated Karen previously.
WHile David and the 5th person were outside my guess is that Reeves walked in on Karen and Saturly making out and lost it. Saturly being shot multiple times points straight to it being a spur of the moment emotional killing.
Reeves then shot Karen in his anger, and by this time David had probably run in and launched into Reeves who then shot him in his rage.
Realizing what he had done Reeves started to leave and then decided to just kill himself.
That's pretty much the way I see it as well. Or something similar. I'm going to speculate Reis was hooking up with Saturley back at the bar (in the presence of her previous boyfriend) and decided to bring him back to her brother's and Reeves' place to continue the fun. At first Reeves likely thought he'd be cool with this but as the night wore on and fueled by jealousy, humiliation, stress and alcohol, Reeves finally lost it when they got home.
Why others here are intent on pursuing a homosexual angle to this story is beyond me.
As a fan of Hercule Poirot, I’d say you have nailed the entire scene accurately, except the activity between Saturly and Reis was probably a bit more ‘active’, to illicit such a murderous reaction.