Firing speed is capped at 0.1s, no questions asked. Otherwise, SoG5 would have 100% firing time reduction, thus you could empty the full pistol magazine in 0.00s whole.
As for reloading and move speed, I believe these are capped as well - but these caps are much harder to reach.
In movespeed case, the fastest man on Mars would probably be a Scout with HR3 wearing a full phaseshift set (both items A-modded) on a AAoLT challenge who is berserk. The movespeed bonuses are multiplied, insated of added, so the resulting speed would be along the lines of 0.30s (0.23s when running, 0,21s when berserk). AAoLT then brings another 30%, so when berserk we would get a movespeed of 0.15s, not reaching the cap.
Reaching reloading speed cap is outright impossible. AFAIK the fastest-realoding weapon is the speedloader pistol with 0.60s. Rel3 would cut this to 0.24s and berserk would cut it to 0,16s. Being a scout on AAoLT in addition would only get you to 0.16s, not reaching the cap.
One thing that can _break_ the cap is being berserk - on my SoG5 run when I picked a Berserk pack, the @ screen told me that my firing speed was 0.07s, so I assume that berserk effect is factored in after the cap is applied. As all actions take some multiply of 0.1s, this would mean that every one of three shots fired _took no time at all_. This may well be an unintentioned behaviour and a bug.
If someone finds a faster movement or reloading example, or if someone finds that I did my math wrong, feel free to correct me, of course.