As far as tzadikim being alive after their passing see NEFESH HACHAIM
Aww, sorry, your argument doesn’t wash. The Rebbe is treated as alive more than any other talmid chochom in history.
I wasn’t saying anyone was moshiach, that has nothing to do with what I wrote
It’s hard to argue that treating the Rebbe as living and reating him as moshiach aren’t related.