I don't know what you mean. http://www.turkishdictionary.net/?word=judge "yargiç" means "judge. Why would you "always" add the possessive suffix? Here the possessive suffix shows that it is a possessor. "yargiçin" means "judge's" or "of the judge" or "of a judge" or "the judge's" or "a judge's" So, perhaps you were not aware that "the judge's secretary" = "the secretary of the judge".
in theory, yes. but if there are two "people" in a sentence, you cannot really omit the personal pronouns or possessive adjectives otherwise it becomes vey difficult to understand and nobody speaks like that. the best way to say that is "senin yargıcın onun sekreteri"
Not a native speaker, but from what I've learned thus far, "Your judge is his/her secretary," could be conveyed with
Yargıcın onun sekreteridir.
Manisa Turkish has a really good page on possessor/possessed relationships, which is what is required in such a sentence. You can link to it here:
Hope that helps.