Finding homomorphisms

Question

Let $G$ be the dihedral group of order 14. In the following, justify your answer.
1. Let $A=C_2$ be a cyclic group of order 2. Find all homomorphisms $G→A$.
2. Let $B=C_7$ be a cyclic group of order 7. Find all homomorphisms $G→B$.

Homomorphism definition:
Suppose that $G = (G, ·)$ and $H = (H, ◦)$ are groups, and suppose that $φ : G → H$ is a map. Then $φ$ is a homomorphism of these groups if $$φ(a·b)=φ(a)◦φ(b)$$ for all $a,b∈G$.

Answer 1

Hint :Let $f:G \to A$ be a homomorphism, then for all $a \in G,\quad o(f(a)) \mid 2 $ and $ o(f(a)) \mid 14$, so $o(f(a))=1$ or $o(f(a))=2$

Answer 2

If $f\colon G\to A$ is a homomorphism, then $|G|/|\ker f|$ divides $|A|=2$, so either $\ker f=G$ and the homomorphism is trivial, or $|\ker f|=7$. How many normal subgroups of order $7$ does $G$ have?

If $f\colon G\to B$, by the same reason either $f$ is trivial or $|\ker f|=2$. How many normal subgroups of order $2$ does $G$ have?