How single elements belong to partition though they can't satisfy equivalence relation?

Question

Let $A = \{2, 3, 5, 15\}$ and $G$ is the equivalence relation of elements divisible by 3 and $H$ is the equivalence relation divisible by 5.
Now the quotient set $A/G = \{\{3, 15\}, \{5\}, \{2\}\},$
quotient set $A/H = \{\{5, 15\}, \{3\}, \{2\}\}$.

1. 3$G$15 is valid relation, but how come 5$G$5 and 2$G$2 belongs to quotient set or partition though they are not divisible by 3 ? and what is the intuition benhind including elements those doesn't satisfy the relation ?

2.If we have to calculate the composition of relations,i.e, $(G\circ H)$ do we have to consider single elements that doesn't satisfy the relation?
To simplify, what will be the value of $(G\circ H)$ ?
a). $G\circ H = \{\{5, 15\}, \{5, 3\}\}$
or,
b). $G\circ H = \{\{2, 2\}, \{3, 3\}, \{5, 5\}, \{15, 15\}, \{15, 3\}, \{5, 15\}, \{5, 3\}, \{15, 5\} \}$

3. What is the quotient set $A/(G\circ H)$ ?