Which of the following statements is correct?

Fill in the blanks:
$(1)$ If $t_{1/2} = \frac{0.693}{k}$,then the order of reaction is .......... .
$(2)$ For a zero order reaction,$t_{1/2}$ is proportional to .......... of the initial concentration.
$(3)$ In a first order reaction,the rate of reaction is proportional to the .......... exponent of the concentration of the reactant.

The consecutive reaction $X$ $\longrightarrow Y$ $\longrightarrow Z$ takes place in a closed container. Initially,the container has $A_{0}$ moles of $X$ (and no $Y$ and $Z$). The plot of total moles of the constituents in the container as a function of time will be:

$A$ person's wound was exposed to some bacteria and then bacteria growth started to happen at the same place. The wound was later treated with some antibacterial medicine and the rate of bacterial decay $(r)$ was found to be proportional to the square of the existing number of bacteria at any instance. Which of the following set of graphs correctly represents the 'before' and 'after' situation of the application of the medicine?
[$Given: N = \text{No. of bacteria}, t = \text{time}$, bacterial growth follows $1^{st}$ order kinetics.]

Under identical reaction conditions,the concentration of a substance is $1.386 \ mol \ m^{-3}$. It is halved in $40 \ s$ and $20 \ s$ by first-order and zero-order kinetics,respectively. The ratio of the rate constants for the first-order $(k_1)$ and zero-order $(k_0)$ reactions,$\left( \frac{k_1}{k_0} \right)$,is ............ $m^3 \ mol^{-1}$.

If the half-life periods of a first-order reaction and a zero-order reaction are equal,then the ratio of the initial rates of the reactions will be .............