Statement (1) is accurate; for zero-order reactions, the rate is unaffected by reactant concentration.
Statement (2) is also correct; the half-life of a zero-order reaction, $t_{1/2} = [A]_0 / 2k$, demonstrates an inverse relationship with the rate constant.
Statement (3) is incorrect because molecularity, defined as the count of reacting molecules, cannot be zero in a valid reaction.
Statement (4) is true; for a first-order reaction, the half-life is $t_{1/2} = 0.693/k$.
Therefore, statement (3) is false.