The numerical method used by F.X Wortmann for inverse design
What is the $(t)$ in $\bar{y}_n^{(t)}$ in (A-2)


The text doesn't say. t in German normally denotes chord (Tiefe), but since we later see $\bar{y}_n^{(s)}$ for the camber line (Skelettlinie), it here stands for Tropfen, denoting the thickness distribution of the uncambered airfoil.

I would also interpret the long dash between $\bar{y}_n^{(t)}$ and the sum in A2 as a misprinted equal sign. Otherways the whole sequence will not add up.


  what is the $p^{th}$ approximation in (A-3)


You mean $p$th, don't you? p is used as the index of a stepwise approximation. $f_m^{(p)}$ is the $p$th iteration of $f_m$.


  What is the $(s)$ in $\bar{y}_n^{(s)}$ in (A-2)


That is only in A 6 and indicates that $\bar{y}_n$ this time denotes the ordinate values for the camber line (see above).


  Does (A-6) refer to the camber line calculation?


Yes.