Tell me please, is the autopilot still "in charge" or does manual flying take over, can the autopilot react that quickly to counter very violent turbulence?
You would generally leave the autopilot in. However if the turbulence is very severe it sometimes won't allow you to engage it as it keeps tripping out. The recommendation would be to leave it in. However the autothrust/autothrottle (i.e the automatic accelerator) would be taken out if it is very bad to stop the sudden power increases and decreases as the aircraft bobs up and down.
Turbulence is not dangerous, only uncomfortable. It's no different to a boat bobbing up and down on a wave. CAT is exactly that, waves in the upper atmosphere. The aircraft simply goes up and down these. One thing to note however is that an aircraft dosen't drop hundreds of feet. You have to consider that a modern jet aircraft cruises at between 500 and 550mph. Every time it hits one of these bumps it always feels alot worse than it is. It's no different to a car hitting a speed ramp at speed. If you slow the car down, then it dosen't feel as bad. Thats exactly what pilots do when they encounter turbulence, they slow the aircraft down to make it more comfortable.