Yes, Epstein killed himself.
The NYC medical examiner ruled it a suicide: https://www.nytimes.com/2019/08/16/nyregion/jeffrey-epstein-autopsy-results.html
Attorney general William Barr called it a "perfect storm of screw-ups" after being initially suspicious that it might have been a murder: https://www.nytimes.com/2019/11/22/nyregion/william-barr-jeffrey-epstein-suicide-investigation.html
DoJ and FBI investigation into Epstein's death resulted in 2 prison guards being indicted for falsifying records - basically that they said they checked on Epstein regularly while instead they took naps and shopped online: https://www.nytimes.com/2019/11/19/nyregion/epstein-prison-guards-arrested.html
Probably the best source of what happened is the indictment of Michael Thomas and Tova Noel, the prison guards on duty the night Epstein died. Here are select parts:
The full indictment can be found here:
Allegedly there is video of the night in question showing no one entered the unit, but I've not been able to find that yet. Hopefully it will be released at some point.
To summarize: Epstein was put in a single cell, the guards stayed outside of the unit, and, allegedly, video footage shows nobody entered the tier where Epstein was housed. Then at 6:30 am the guards entered the tier, found Epstein dead with a noose around his neck and triggered the alarm at 6:33 am.
Given the evidence as it's known now, this is clearly a suicide.