What does a tzaddik mean? there is letter too. can everyone be a tzaddik or not? are there fake tzaddikim? how to differentiate who is fake or not? thank you.

A tzaddik is a righteous person: one who is well-learned in Torah, observes all of the mitzvot, and has sterling character traits. In short, great to God, to his fellow Jews and to the nation of Israel. There is obviously no "course" or official ceremony declaring this status, but it's a common well-deserved recognition by one's society (although sometimes, he may succeed for a while in humbly hiding his special level from his surroundings, it's just a matter of time until he is "discovered", for by definition, he actively helps not only individuals, but also his community and nation). He has no ulterior motives, and accordingly, it can't be "faked", for decades of all-day Torah study, constant acts of kindness, high-level public Torah lectures constantly scrutinized by our classically "critical" Jewish brethren (!), can only be genuine. One of the strong complaints against the Hassidic movement is that they sometimes view their rebbe as an "institutionalized" status, passed down automatically from the well-deserved original tzaddik to his son, and then to his grandson, without having been "earned" and objectively recognized and judged by the masses. On the other hand, there are obvious advantages to one who has been raised by a tzaddik, and sees his father's righteousness up close on a regular basis, and can ask, learn and be influenced by him in the most intimate and unfiltered way.