A) If you consider the case where x>0, y>0 then -x is negative as x is some positive number.
If you consider the case where x<0, then -x>0. Not always true.

B) If you consider the case where x<0, y must be some positive integer greater x (ex: x=-2, y must be at least 3 so that the second inequality x+y>0 holds). In this case, as y is some positive number, -y will always be negative.
The other case is where both are positive integers, and again y will be negative. Always True.

C) Simply move the first inequality (x-y)<0. Always true.

D) (x-y)^2 will always be >=0, so it can never be negative

E) 2x-y
Consider the case where x=4, y=5
and the case where x=-5, y=6. Not always true.

B and C are always true, and are therefore the correct options.