Re. "two orthogonal forces aren't related and two orthogonal vectors don't affect each other"

Your equation $F_s = F_n\cdot c$ is not a vector equation. $F_s$ and $F_n$ are both scalars. If they were vectors and were orthogonal the equation would be mathematically incorrect.

Re. "two orthogonal forces aren't related and two orthogonal vectors don't affect each other"

Your equation $F_s = \mu_s F_n$ is not a vector equation. $F_s$ and $F_n$ are both scalars. If they were vectors, and were orthogonal, the equation would be mathematically incorrect.

Re. "two orthogonal forces aren't related and two orthogonal vectors don't affect each other"

Your equation Fs = Fn*c is not a vector equation. Fs and Fn are both scalars. If they were vectors and were orthogonal the equation would be mathematically incorrect.

Re. "two orthogonal forces aren't related and two orthogonal vectors don't affect each other"

Your equation $F_s = F_n\cdot c$ is not a vector equation. $F_s$ and $F_n$ are both scalars. If they were vectors and were orthogonal the equation would be mathematically incorrect.