Are there really 36 hidden tzadikim? What level are they on (tana, amora, etc.)?
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The Tanya talks about this concept I do not remember them being ascribed a level. It is more that the world exists on their tzidkus or righteousness, The Source is A Gemara see the Wiki: As a mystical concept, the number 36 is even more intriguing. It is said that at all times there are 36 special people in the world, and that were it not for them, all of them, if even one of them was missing, the world would come to an end. The two Hebrew letters for 36 are the lamed, which is 30, and the vav, which is six. Therefore, these 36 are referred to as the Lamed-Vav Tzadikim. This widely-held belief, this most unusual Jewish concept is based on a Talmudic statement to the effect that in every generation 36 righteous "greet the Shechinah," the Divine Presence (Tractate Sanhedrin 97b; Tractate Sukkah 45b). 
As long as you accept the definition of the Lamed Vav Tzadikim, then you "must" believe that there are 36 of them, only if you believe the world still exists. I suppose if you accept the possibility that that the world "does not truly exist" and that its something artificial like as portrayed as in "The Matrix".
So lets pray that these Lamed Vav Tzadikim continue to exist, so that we as well continue to exist.