Option (1) is true because, for zero order reactions, the rate is independent of the concentration of reactants.
Option (2) is also correct as the half-life for a zero order reaction is given by $t_{1/2} = [A]_0 / 2k$, which is inversely proportional to the rate constant.
Option (3) is false because molecularity refers to the number of reacting molecules and cannot be zero for a valid reaction.
Option (4) is true as for a first order reaction, the half-life is given by $t_{1/2} = 0.693/k$.
Hence, the false statement is (3).