Use the half-life dependence on initial concentration

For an $n$-th order reaction ($n\neq 1$), $t_{1/2} \propto \frac{1}{[A]_0^{\,n-1}} = [A]_0^{\,1-n}$

So if $t_{1/2} \propto [A]_0^{m}$ then $m=1-n \quad \Rightarrow \quad n=1-m$

Infer relation from the given table

From the table, $t_{1/2}$ increases as $\sqrt{[A]_0}$, i.e. $t_{1/2} \propto [A]_0^{1/2}$

Therefore, $1-n=\frac12$ $n=\frac12$

Hence statement A is true.

Find the proportionality constant

Since $t_{1/2}=k'\sqrt{[A]_0}$ using the tabulated data, the constant comes out to be $k'=200\sqrt{10}\ \text{min M}^{-1/2}$

Therefore, for $[A]_0=1\,\text{M}$, $t_{1/2}=200\sqrt{10}\times \sqrt{1}=200\sqrt{10}\ \text{min}$

So statement B is true.

Check statement C

Reaction order is a property of the rate law under given conditions; it does not change merely because concentration changes from $0.100\,\text{M}$ to $0.500\,\text{M}$.

So statement C is false.

Check statement D

For $[A]_0=1.6\,\text{M}$, $t_{1/2}=200\sqrt{10}\sqrt{1.6}$

Now, $\sqrt{10\times 1.6}=\sqrt{16}=4$

Hence, $t_{1/2}=200\times 4=800\ \text{min}$

So statement D is true.

Select the correct option

True statements: A, B, D

Therefore the correct option is: $\boxed{\text{B: A, B and D Only}}$