Mr. X is the engineer and either his wife or his son is the Doctor.
Mr. X's wife and mother are not blood relatives.
From 3, then, if the engineer is a female, the doctor is a male. However, from 1, if the doctor is a male, then the engineer must be a male.
Thus, there is a contradiction, and the engineer cannot be female (either Mr. X or his son is the engineer).
Mr. X's son is the youngest of all four and is blood relative of each of them.
So, from 2, Mr. X's son is not the engineer.
Hence, Mr. X is the engineer.
Now, Mr. X is the engineer, and obviously he is both younger than his mother and a blood relative to her.
From 2, then, Mr. X's mother can not be the doctor.
So the Doctor is either his wife or his son.
It is not possible to determine anything further, or eliminate either of these possiblities.
Also, it does not even mater (for statement 2) if Mr. X or his wife are younger or older, as either way they are not blood relatives.