Which of the following relations is correct for the given reaction orders?

For any chemical reaction,what factors do chemists aim to determine?

Select the incorrect statement.

For the following parallel chain reaction,what will be the value of the overall half-life of $A$ in minutes?
Given that $\frac{[B]_t}{[C]_t} = \frac{16}{9}$
$A \xrightarrow{k_1 = 2 \times 10^{-3} \ s^{-1}} 4B$
$A \xrightarrow{k_2} C$

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.

At $100\,^\circ C,$ the gaseous reaction $A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$ is found to be first order. Starting with pure $A,$ if at the end of $10\,\min$,the total pressure of the system is $160\,mm$ and after a long time,when dissociation of $A$ was complete,it was $300\,mm.$ The partial pressure of $A$ at the end of $10\,\min$ is .......... $mm$