The elements in $\mathbb Z[x]/$ are equivalence classes represented by polynomials of degree less than $3$. So, formally speaking, none of the elements you list are in $\mathbb Z[x]/$. However, these elements do represent elements in $\mathbb Z[x]/$. The elements you list all represent different elements in $\mathbb Z[x]/$ but not all of them. You are missing $2$ more polynomials: $x^2+x$ and $x^2+x+1$. This will give you a complete list of representatives.
In general, given a polynomial $p(x)\in F[X]$, where $F$ is a field, the ring $R=F[x]/$
has cardinality $|F|^d$ where $d$ is the degree of $p(x)$. Every element in $R$ is an equivalence class of the form $q(x)+$
, and a complete list of representatives is given by all polynomials in $F[x]$ of degree smaller than $d$.