a) AlCl₃ fumes in moist air due to its hydrolysis
b) Al metal is stable in dry air because of protective oxide layer.
c) pπ - pπ back bonding does not occur in halides of aluminium because of larger size.
d) AlCl₃ achieves stability by forming a dimer.
Correct statements are

→ Sizes of Al and Cl are large, therefore in between the Al and Cl "π" bond formation is not possible.

→In order to get octet configuration around the "Al" AlCl₃ undergoes dimerisation and forms Al₂Cl₆  dimer

AlCl₃ achieves stability by forming a dimer.

        

→ Anhydrous AlCl₃ fumes in air.

White fumes appear around the bottle of anhydrous aluminium chloride.
 Anhydrous aluminium chloride is partially hydrolysed with atmospheric moisture to liberate HCl gas. Moist HCl appears white in colour.

→ It has 4  Al—Cl terminal bonds and 2 Al—Cl bridge bonds.

Al—Cl bridge bond length > Al—Cl terminal bond length.

→ Bridge bond is non electron deficient bond i.e.,3C — 4e¯ bond.

→ In vapour state and in non polar solvents anhydrous AlCl₃ exist as dimer and shows covalent nature and acts as non conductor.

→ In polar solvents like H₂O dimer undergoes cleavage by hydrolysis and forms  complex compound.

It shows ionic character and acts as conductor in polar solvents.

→ Al metal is stable in dry air because of the formation of protective oxide layer on its surface.