A) constant 0 is a kernel, constant 1 is a kernel, too. But 0-1=-1 is not PSD.
Thus false IMHO.
B) Assuming 2D data, where x=0 for Class 1, x=1 for Class 2, and y is uniformly random. Any vector from each class is as good a support vector as the others, yielding the same hyperplane. Visually:
x1 | y1
|
x2 | y2
Which SVM is better, the one using x1 and y1 as support vectors, or the one using x2 and y2?