A.
believes that clinical depression, along with several other mental illnesses,
are exacerbated by
Subject "Practitioners" doesn't agree with the verb "believes" in number. Also note that "along with several other mental illnesses" is a modifier and doesn't change the number of the subject "clinical depression". Hence the use of "are" is wrong.
INCORRECT_____________________________________________________________________________________________________________
B.
believe that clinical depression, along with several other mental illnesses,
is exacerbated by
All the subject verbs agree in number and the verb tense usage makes sense.
CORRECT_____________________________________________________________________________________________________________
C. believe that clinical depression, along with several other mental illnesses,
are exacerbated by
subject "clinical depression" doesn't agree in number with verb "are"
INCORRECT_____________________________________________________________________________________________________________
D.
believed that clinical depression, along with several other mental illnesses, is
exacerbated in
The two verbs "believed" and "exacerbated" are states in simple past making them parallel and changes the sequence.
INCORRECT_____________________________________________________________________________________________________________
E.
had believed that clinical depression, along with several other mental illnesses,
has been exacerbated by
use of past perfect tense without a related simple past event is
INCORRECT_____________________________________________________________________________________________________________
Hence option B