Fastest 0 hit time. Can have sub categories of any% and 112%

If you mean with the Glass Soul mod installed, that would go into https://www.speedrun.com/hkmods

There are people who do hitless runs, which usually involves having a minimum-hits PB rather than a 0-hit speed PB. 0-hit is hard enough without worrying about speed. If you join the Discord (linked from this page), there is a #hitless channel where you can discuss

Have you done any 0-hit runs yourself?