You are overlooking that all the residents gather together each day. Once a visitor has said something nontrivial, after that the new information each day comes when the residents gather, and discover who did or didn't commit suicide the night before.

Also:

> For instance, if the number of blues is 25, and the (merciful) stranger says that the number of blues is not prime every day, no one ever has enough information.

This is not correct. Saying "the number of blues isn't prime" just once would be sufficient to start the process, as would "there is at least one blue", etc. It doesn't matter that it's not new information to any one villager.