Does every 3CNF propositional formula has an equisatisfiable 2CNF propositional formula Does every 3CNF propositional formula has an equisatisfiable 2CNF propositional formula?
Yes.  If the 3CNF formula is satisfiable, here is an equisatisfiable 2CNF formula: True.  If the 3CNF formula is not satisfiable, here is an equisatisfiable 2CNF formula: False.  So yes, every 3CNF formula has an equisatisfiable 2CNF formula.

If you want to actually find that formula in a reasonable amount of time, then we don't know of any way to find such a formula in polynomial time (existence of such a method would prove that P = NP).