SDK^ said:
Especially as some of those sparks are dangerously close to those overhead lights
If you look closely you can see the fluorescent tubes glowing from the EM radiation given off by them.
As for the henry it was used to cool the spark gap that is needed for these coils. These turn the electricity into pulses and thus allow for the long arcs. The big coil learnt the hard way about this as the spark gap got fried on the record breaking run.
Yes the event are dangerous, but only if your stupid, it isn't open to the public (for a good reason) but as long as you don't touch anything you'll be fine. Due to the poles on the top of the big coil the arcs were only going in one direction.