A is the only daughter of B, C is the husband of B, D is the father of C and E is the wife of D. How is A related to E?

B and C are a married couple, and A is their daughter.
D is C's father and E is D's wife, so E is C's mother.
E is therefore A's grandmother, which makes A her granddaughter.
Note: A is explicitly a daughter, so "grandson" is ruled out by the wording, not by the tree.

M is son of A. R is daughter of V. S is sister of M and R. B is married to S and K is son of B. M is the only brother of S and R. L is daughter of R. How is L related to A?

"M is the only brother of S and R" makes M, S and R siblings.
M is A's son, and R is V's daughter — so A and V are the parents of all three.
L is R's daughter, one generation below R, which puts her two generations below A.
L is A's granddaughter.
Note: B and K are there purely as noise. Not every name in the question is needed.

Pointing to a man in a photograph, A said, "His daughter's mother is the daughter-in-law of my father". How is A related to the man?

"His daughter's mother" is the man's wife.
She is the daughter-in-law of A's father, so she is married to a son of A's father.
That son is the man himself — therefore the man is A's brother.
A is his sibling.
Why not "brother"? A's own gender is never given. The answer has to be the gender-neutral "sibling", and this is exactly the distinction the options are testing.

In a family of eight: D is the grandson of F, G is the son-in-law of C, F is the mother of B, A is the wife of B, H is the daughter of C and the mother of D. Who is the father of D?

H is D's mother, so D's father is H's husband.
G is the son-in-law of C, meaning G married a daughter of C.
H is the daughter of C — so G is married to H.
D's father is G.
Method: "son-in-law of X" is always the entry point in these puzzles, because it fixes a marriage without naming it directly.

Pointing to a covered photograph, a man said to his brother-in-law, "She is the mother of my father's daughter". How is the person in the photograph related to the brother-in-law?

"My father's daughter" is the man's sister; her mother is the man's own mother. So the photograph shows the speaker's mother.
The listener is the man's brother-in-law — that is, the husband of the man's sister.
The speaker's mother is his sister's mother, and to her husband she is his mother-in-law.