These are easy on paper and nearly impossible in your head, which is the whole design of the question. Two minutes of careful drawing beats twenty seconds of confident guessing.
Use one consistent notation and generations on separate rows. Most wrong answers come from losing track of which generation somebody is in, not from the logic.
Try each one before opening the answer. A solution you have read is not a solution you can produce under time pressure, which is the only kind that counts.
Q1 Pointing to a photograph, a man says: "She is the daughter of the only son of my grandfather." How is she related to him?
His sister.
The grandfather’s only son must be the speaker’s own father - if there were another son, the father would not be the only one. So she is his father’s daughter, which makes her his sister.
Q2 A is B’s brother, C is A’s mother, D is C’s father and E is D’s mother. How is A related to D?
Grandson.
Row by row: E is at the top, D is E’s child, C is D’s child, and A and B are C’s children. So D is A’s mother’s father - A’s grandfather - and A is therefore D’s grandson.
Q3 If P is the sister of Q, Q is the wife of R and R is the son of S, how is P related to S?
Daughter-in-law’s sister - no direct blood relation to S.
S is R’s parent. Q married into the family, so Q is S’s daughter-in-law. P is Q’s sister, which makes P related to S only by marriage, not by blood. "Sister-in-law" is the loose answer people give and it describes P’s relation to R, not to S.