Ask yourself, what would happen to our nuclear power plants in an EMP attack? I'll go with total meltdown - across the country.
Ask yourself, what would happen to our nuclear power plants in a lightening strike?
Keyword: electronic circuit breaker
Nuke plants should be very well protected from gamma due to all the rebar and metal in the outer buildings. The control systems would essentially be protected by multiple Faraday cages.
A very interesting question. At Fukushima, I think the earthquake didn't do anything really massive to the nuclear plants. And I think the tsunami didn't do anything really massive to the nuclear plants. But those events did create a power outage and the power outage led to meltdowns.
I don't think Japan expected such a turn of events, and it is not clear to me that America has either.
All our serious enemies (Iran, NK, Chavez, Castro,...) understand that successfully delivering a high EMP yield weapon would be a knockout blow. We would be left with our submarines. They could destroy all our enemies. That should be made clear to the Russians and Chinese. They may be able to knock out our electric grid, but they will have nothing left but smoldering craters.
Most likely nothing would happen to the nuke plant itself. They would lose the external infrastructure such as transformers, generators, and other devices which are not protected. They’ll be forced to shutdown though as the system to distribute the electricity would be heavily damaged.