Identify the incorrect statement from the following :

Atomic radius decreases across a period from left to right, so the atomic radius of $\text{Mg}$ is greater than that of $\text{Al}$.

For isoelectronic species, the ionic radius decreases with an increase in nuclear charge. Both $\text{Mg}^{2+}$ and $\text{Al}^{3+}$ have $10$ electrons, but $\text{Al}^{3+}$ has a higher nuclear charge ($Z=13$) compared to $\text{Mg}^{2+}$ ($Z=12$), making $\text{Al}^{3+}$ smaller than $\text{Mg}^{2+}$.

Cations are always smaller than their respective parent atoms. Therefore, the overall decreasing order of size is $\text{Mg} > \text{Al} > \text{Mg}^{2+} > \text{Al}^{3+}$. The largest species is $\text{Mg}$ and the smallest is $\text{Al}^{3+}$. Thus, statement (1) is incorrect.

For atomic number $107$, the IUPAC roots are un ($1$), nil ($0$), and sept ($7$), giving the name Unnilseptium. Statement (2) is correct.

Lithium and Magnesium exhibit similar properties due to their comparable polarizing power (charge-to-size ratio), which is known as a diagonal relationship. Statement (3) is correct.

In the complex $[\text{AlCl}(\text{H}_2\text{O})_5]^{2+}$, let the oxidation state of $\text{Al}$ be $x$. We have $x + (-1) + 5(0) = +2 \Rightarrow x = +3$. The central metal atom is surrounded by $6$ ligands ($1$ chloride and $5$ water molecules), so its covalency is $6$. Statement (4) is correct.

Answer: The largest and the smallest species among Mg, $\text{Mg}^{2+}$, Al and $\text{Al}^{3+}$ are Al and $\text{Mg}^{2+}$, respectively.