Regarding only one answer possible


#1

can’t 3, 4 be the answer as well or any other pair of integers.


#2

Same is my suggestion regarding this


#3

No, it is never else possible, since S can’t deduce the answer after P denies he knows too, since there will be many possibilities even for x = 3,y = 4 so S would have got 7, hence he will think how 7 can come,
1 + 6; 2 + 5;3 + 4.