1. eliminate this one with a simple numeric example:
x = 3.5
y = 1.5
While x + y = 5 - integer and x - y = 2 - integer, y is not an integer.

But take:
x = 2
y = 1
This time, x + y, x - y and y are all integers.

2. x + 2y is an integer helps you since you know that x + y is also an integer. x + 2y = (x + y) + y and since what you have in the parentheses is an integer, y must also be an integer.

For St 2 if I take

3 + 2 * 2.5 = x + 2y = 8 = Int.

But x + y = 3 + 2.5 = 5.5 = Not an Integer.

Won't C be OA here?

For St 2 if I take

3 + 2 * 2.5 = x + 2y = 8 = Int.

But x + y = 3 + 2.5 = 5.5 = Not an Integer.

Won't C be OA here?

In the case above x+y will not be an integer as given in the problem

3+2.5 -> not an integer

Hope this helps.