The C is a carrier variant with a stronger landing gear intended for carrier landings as well as larger foldable wings.
Both services will operate the F-35c with the FAA operating from naval platforms. The new carriers have had their designs changed to incorporate an arrestor wire for that very purpose.
While I can't comment on workload I think it is practical to have Navy personnel working on the project considering most will be ex-Harrier, who have experience of fixed wing carrier based ops and who also now have a lot of time on their hands with no airframe to fly.
Should be interesting to see how the skill of carrier landing will be picked up; after a 4 year hiatus of all fixed wing activity. I can only imagine with a lot of sim time.