Lot's to unpack here. But...to answer your question about "If there is one outlier (a non-parallel response)...does this impact the whole output? ". Yes, one bad actor can reject (p-value < 0.05, say). your parallelism test. And, FWIW, this is the "old" way of determining parallelism. The most appropriate way is to test for equivalence between model parameters (for parallelism in the 4p logistic model, this is growth rate, and asymptotes). This can be done via the Equivalence Test option in the red triangle pull down menu of the Fit Curve results. Therein, you can also define your equivalence bounds for the ratio (Decision Limits as they are called in the Fit Curve platform). If desired, you can look at all pairwise comparisons (caution: if you have 20 curves, that is 190 pairwise comparisons) if you perform the equivalence test several times since you have to choose a reference curve (reference will be in the denominator of all confidence intervals for ratios). Equivalence testing tests for practical equivalence (ratio within Decision Limits) rather than a difference (as tested via the p-value for parallelism). i.e., "are the curves 'parallel enough' such that any differences are of no practical significance?" is the appropriate question, rather than "are they different"?. As I said, there is a lot to unpack here; there is a load of info out there on testing for parallelism, and see attached for a fairly readable explanation on the details.
