For any of the speed runs is mobile allowed or is this a pc only?

Yes, mobile is allowed!

what if your device is super slow. i use an old Samsung tablet, so it has very low fps, which but my timer is a good 60(ish) fps.

Also i do have a suggestion for a category: "All npcs" category, including the underground skeleton (which i haven't seen in many years, to the point i feel it was removed)

Low FPS can cause the game to literally run slower, which is likely only a disadvantage. I believe using the option Frame Skip ON should fix this, so use that to be safe.