When I purchase a cleaner wrasse, I buy ones from Sri Lanka as I've had no real problems with ones from there. I can't say that about other sources as I test the wrasses before I buy and it's pretty consistant, but not totally so, that Sri Lanka ones will eat in the LFS tanks before I buy them. From other areas, they usually don't eat my test food that I place in the LFS tanks, but on occasion they have.
I used to use a blend of foods for my test food, but then went strictly to using ground up beef heart. When ground up to very small size particles, like newborn brine shrimp, I've never seen a Sri Lankan one not eat this food. So if all else fails and you have a problem getting a new one to eat, try ground up beef heart. All my cleaners go on to eat all foods I place in the tanks that are appropriately sized for the size of the cleaner. (There mouths are small so krill for instance are too large a particle for all the the largest of the cleaners)
Within a short time, all my cleaners eat spirulina flake food as their main food.
As for cleaning fish, I'm not sold on the cleaner wrasse as a prevention for the dreaded ich as many years ago when I had an ich problem in one tank, the cleaner in that tank, while he appeared to eat something off the fish, he didn't clean off visible parasites at that time, and, some fish don't allow the cleaner to clean them.
For me, when I started purchasing them, it was like my very first purchase which was a clown and sebae anemone, for the relationship to be able to watch the interaction between clown and anemone, cleaner wrasses and fish.