Yes, in normal (auto) mode the ECLs can shut down the engines.
Yes, in Manual ,mode they control the engines like most other aircraft.
If the EECs fail which I believe would include a loss of electrical power, then the engines revert to manual control automatically.
The fire seems to have had more impact on the ability to change collective pitch than control over the engines but I don't know what connections are involved in that wiring bundle that was chafed, nor what effect those wires shorting out would have on the rest of the electrical system.
The best thing is that the crew are on the ground safely to give feedback on the emergency(s) that they had to deal with rather than us waiting for the FDR to produce answers long after the event.
I hope their pax bought them a lot of beer.