About a symmetric rank decomposition of a SYM◦SYM circuit's truth table matrix
The fact that the same letter is used twice doesn't mean that it signifies the same thing. In particular, in your first question, clearly $a \in \{0,\ldots,s\}$ and $b \in \{0,1\}$, whereas in the second question, it is explicitly stated that $a,b \in \{0,\ldots,t\}$. From your excerpts, it seems that the second $a,b$ are of the same "type" as the $a$ in your first question.

Your third question is unanswerable given your excerpts. It could be that the construction is instantiated with several different values of $t$. In any case, I would look at the place in which the construction is invoked to find out what the value of $t$ should be.