Conjunctive normal form to simple elementary algebra
$\mathsf{P}$ and $\mathsf{NP}$ are classes of decision problems. Essentially, a decision problem is a function $D \subseteq \{0,1\}^\ast \times \{ 0,1 \}$ (although describing $D$ simply by giving the subset $\{ 0,1 \}^\ast \times \{ 1 \}$ is more common). A Turing machine is said to solve $D$ if, given any string $x \in \{ 0,1 \}^\ast$, it produces $D(x)$. If there is a Turing machine which does so in time bounded by a polynomial $p(|x|)$, then $D \in \mathsf{P}$. If there is a nondeterminstic Turing machine capable of doing so in polynomial time, then $D \in \mathsf{NP}$. As you can see, $\mathsf{P}$ and $\mathsf{NP}$ are unrelated to transforming representations of objects into other (equivalent) representations; they are only about saying, for some string $x$, whether $D(x) = 1$ or not.

In your case, what we can do is analyze the time complexity of each transformation.
The step CNF $\to$ AFF simply causes the formula to be longer by a constant factor and can be realized in linear time.
In AFF $\to$ EAF, the formula blows up exponentially; assuming we previously had a maximum of $t$ terms for each of the $c$ clauses, you go over every possible $t^c$ multiplication of said terms, which takes potentially exponential time.
The final EAF $\to$ SEAF step aggregates some terms and may be computed, for instance, in quadratic time (e.g., by looping over each term in the formula).
Note that these time complexities are all relative to the respective input length for each step; for instance, "linear" is supposed to mean bounded by $c |\varphi|$, where $\varphi$ is the respective formula which is given as input to the respective transformation step.

I am not aware of a name for the forms you have given. Nevertheless, considering a Boolean formula $\varphi$ as an arithmetic expression (in particular over larger fields) is usually referred to as an arithmetization of $\varphi$ and is very relevant in complexity theory; see, for instance, this and this.