That's not correct:

"[I have performed normality test and it isn't normally distributed,] thus I can't use parametric test (ANOVA 2 way, etc)."

Firstly, a "significant" test of normality is not neccearily indicating that the assumption of normality is unreasonable and would lead to invalid conclusions. It depends on the character of the deviation from normality and on the sample size. Generally, formal tests of normality using the "significance" of such tests to decide whether or not the normal assumption of a subsequent analysis is justified is almost complete nonsense. Your decision to use a normal distribution based test would be based on "failing to reject the null hypothesis", what is a clear no-go.

Secondly, there may be a more appropriate stochastic model than the normal-distribution. If depends on the kind of the variable you are analyzing. There are many other parametric models available (for counts, proportions, concentrations/intensities, waiting times, etc). And sometimes it's also possible to use a (sensible) transformation to have an approximate conditional normal distruibution of the transformed variable. A natural choice for positive, continuous measures is usually the log-transformation, for instance.

Friedman test cannot be used with a replicated factorial design. It is used for a unreplicated complete block design. (And so, it is not used in the same situation as a two-way anova.) There are nonparametric tests for factorial designs. For a two-way design, there's the Scheirer–Ray–Hare test. You could also use aligned ranks anova. The post-hoc testing will depend on which test you ultimately decide to use.