You could say "May I meet you tomorrow?", and it would be simpler.
But, if you want to use a construction with the infinitive verb, and ask whether it is possible, then sentence #1 is the only acceptable one.
The construction in sentence #2 would be OK to ask about the possibility of a simple thing: "Is a meeting possible?" , but the whole infinitive verb-phrase, "to meet you tomorrow" is just too long to fit in there gracefully (without sounding awkward).
This is why we use the dummy pronoun or placeholder pronoun "it": "Is it possible to meet you tomorrow?"
It simplifies the main sentence to: "Is it possible?", and follows up with the definition of "it" at the end.
Sentence #3 also uses a dummy/placeholder, "there". "There" is similar to "it" but you use "there" only to inquire about the existence of something. "Is there a possibility?" [Does a possibility exist?]
So you could also say, "Is there a possibility to meet you tomorrow?", but the nicest sounding question is #1.