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

Anhydrous aluminium chloride is hydrolysed partially with the moisture in the atmosphere to give HCl gas. 

This HCl combines with the moisture in the air and appears white in colour.

Al_2​O₃​ is formed which forms a protective layer on the metal

AlCl₃ lacks back bonding as in BCl₃ because of increase in size of aluminium.