What is the unit of the rate constant for a $4^{th}$ order reaction?

Which of the following statements regarding the molecularity of a reaction is wrong?

For a reaction $2 \ A + B \rightarrow P$, when the concentration of $B$ alone is doubled, the rate does not change, and when the concentrations of both $A$ and $B$ are doubled, the rate increases by a factor of $4$. The unit of the rate constant is,

At $345 \ K$,the half-life for the decomposition of a sample of a gaseous compound initially at $55.5 \ kPa$ was $340 \ s$. When the pressure was $27.8 \ kPa$,the half-life was found to be $170 \ s$. The order of the reaction is $......$ [integer answer]

For a certain reaction,the rate constant $K = 2.37 \times 10^2 \ L^2 \ mol^{-2} \ s^{-1}$. What is the order of the reaction?

Which will be the unit of rate constant for the reaction having Rate $= K[A]^{\frac{1}{2}} \cdot [B]^{\frac{3}{2}}$ ?