I'm fairly new to reef tanks and only had my mushroom for about 2 months now and it hasn't been sick, so I'm not sure what to do for a sick one. I would think that finding the cause of the sickness (poor water quality) would be the solution. Maybe there is an ammonia spike or the PH, temp, or salinity is off. Once the problem is found and fixed, they should come back to normal.
I don't feed them anything. I add some bioplankton every week with water changes. I think all they need is some light and healthy water though.