Identify the key fact:

The reaction is given to be first order.

For a first-order reaction, $-\frac{d[A]}{dt}=k[A]$ and the integrated rate law is $[A]_t=[A]_0 e^{-kt}$

Check Option A:

From $[A]_t=[A]_0 e^{-kt}$ the concentration of reactant decreases exponentially with time.

So, A is correct.

Check Option B:

For a first-order reaction, half-life is $t_{1/2}=\frac{\ln 2}{k}$

As temperature increases, the rate constant $k$ increases according to Arrhenius equation, $k=Ae^{-E_a/RT}$ Hence $t_{1/2}$ decreases when temperature increases.

So, B is correct.

Check Option C:

For a first-order reaction, $t_{1/2}=\frac{\ln 2}{k}$ which is independent of initial concentration.

Therefore, the statement "half-life depends on the initial concentration" is false.

So, C is incorrect.

Check Option D:

After $n$ half-lives, fraction remaining is $\left(\frac{1}{2}\right)^n$

For $n=8$, $\text{fraction remaining}=\left(\frac{1}{2}\right)^8=\frac{1}{256}=0.00390625$

Therefore, fraction completed is $1-0.00390625=0.99609375$ $=99.609375\%$

This is approximately $99.6\%$ completion.

So, D is correct.

Final answer:

Correct options are: $\boxed{A,\ B,\ D}$

Comparison with stored correct answer:

Stored answer: A, B, D

Derived answer: A, B, D

They match.