Sorry, I didn't see this one earlier.
I wouldn't worry too much about the dishwasher on the Eat'n Tool itself, although I'd probably not run the carabiner through as the small spring on the gate might not like the heating, cooling and moisture.
As for the coating, well I doubt there is much to worry about there either. I would imagine it should be pretty safe- if it would wear off that easily then people would complain about it coming off when they eat with it.
Def