The first two follow from the definitions, so I'm assuming you're having some difficulty with what injective (or one to one) and surjective (or onto) mean.
Let $f : A \rightarrow B$ be a function.
Our function $f$ is injective if, provided there is some $a$ in $A$ with $f(a) = b$, there is only one such $a$. Put another way, everything in $B$ that is "hit" by $f$ is "hit" only one time. This is why one-to-one is a good term: for every output, there is one input.
Our function $f$ is surjective if, for every $b$ in $B$, there is some $a$ with $f(a) = b$. Essentially, $f$ is surjective if everything in $B$ is "hit" by $f$. This is why onto is a good term: you can picture $B$ being covered by $f$.
For your part (a), think about functions from ${1,2}$ to $\mathbb{N}$ that do not have the property that "for every output, there is one input."
For your part (b), think about functions from $\mathbb{N}$ to ${1,2}$ that do not have the property that "everything is hit" by the function.
You need to reword part (c); it does not make sense as written.