(Part A)
A prime number is
a number that can be divided by itself AND 1, which means you can only have 2 factors for a prime number.

Think about the factors of 1, only 1 x 1 gives you 1 right ? Which means 1 is its one and only factor, so it cannot be divided by itself AND 1.

Hence, a prime number MUST be more than 1 and so 1 is not a prime number.

0 is not a prime number as 0 divided by itself is undefined.

(Part B)
No. I disagree. A composite number is a positive number that has factors OTHER THAN 1 and itself.

Eg.
4 = 2 x 2 (has factors which is not 1 and 4)
6 = 2 x 3 (has factors which is not 1 and 6)

All whole numbers that aren't prime numbers, are not necessarily numbers that has OTHER factors.

1 is not a prime number, but 1 has only itself as its factor. 0 is not even a positive or negative number.

Hope it helps!