We analyse each statement based on periodic trends described in NCERT:

1. Correct: In the complex $[AlCl(H_2O)_5]^{2+}$, Aluminum is bonded to 1 chloride ion and 5 water molecules, making the coordination number 6. The charge is calculated as $x + (-1) + 5(0) = +2$, so $x = +3$. This statement is factually correct (See NCERT Class 11 Problem 3.9).
2. Correct: $Na_2O$ is an oxide of an alkali metal and is strongly basic. $Cl_2O_7$ is an oxide of a halogen in a high oxidation state and is strongly acidic. (See NCERT Class 11 Section 3.7.3).
3. Correct: Isoelectronic species have the same number of electrons. $O^{2-}$ (8+2=10), $F^-$ (9+1=10), $Na^+$ (11-1=10), and $Mg^{2+}$ (12-2=10) all have 10 electrons. (See NCERT Class 11 Section 3.7.1).
4. Incorrect: Cations are always smaller than their parent atoms due to increased effective nuclear charge holding the remaining electrons. Thus, $Al^{3+} < Al$ and $Mg^{2+} < Mg$. Between the isoelectronic ions $Mg^{2+}$ and $Al^{3+}$, $Al^{3+}$ has a higher nuclear charge (Z=13) than $Mg^{2+}$ (Z=12), pulling the electron cloud tighter. Therefore, $Al^{3+}$ is smaller than $Mg^{2+}$. Generally, atomic size decreases across a period ($Al < Mg$). The overall order of size is $Mg > Al > Mg^{2+} > Al^{3+}$. The smallest species is $Al^{3+}$, not Al. (See NCERT Class 11 Problem 3.5).