When a person does not like another person's comment on a public Facebook page, I suppose the best thing he/she can do is to hide that comment. But when he/she presses the hide link, will this information be notified to the admin? Or can the admin have any way to check who hides the comment?
No, it will not be notified to the admin. And there is no official way to check who hides the comment. When he/she hides a comment, it is just hidden from his/her view, others can still see it. Comment will be visible to the person who wrote it and their friends.