How do they spot players?
Reaction time and accuracy?
How do behaviors such as suppressing, grenade throwing, aiming, etc work?
Through the Force
Faster than a double clutch gearbox's shifting time (this is actually not even a joke)
It doesn't. They don't care if they get shot.
Grenades upon leaving the bots' hands immediately turn into a heat seeking missile that disguises itself as a grenade. The missile will find it's way through door locks, cracks and spatial wormholes to arrive on target with impeccable precision.