... as said by Dave - fault would be with the drivers who ran into the back of the car ahead.
... too fast, probably within the speed limit
... too close, probably
... not being fully attentive - yes
... dash cam would be of little use in the first car other that would notice a jolt, would be incriminating for any of the three cars - only possible case of dash cam being useful would be a rear-facing one in the first car, or perhaps the next two as well.
... I have been in Liverpool today and had many instances where traffic lights turned to amber as I approached but with plenty of time for me to stop without braking sharply, yet I saw many cars go through (it was two lanes) on amber and sometimes on red - my dash cam would probably show them up ... what would you do? There were no accidents or near-misses.