Is it ok to have log transformation in difference-in-differences model? It seems like we cannot as it violates the additivity assumption. Am I correct?
Can I assume you mean log transform the outcome? This is certainly an appropriate approach if your outcome is not normally distributed. When you do so, the difference-in-difference estimator (the coefficient on the interaction term [between "treatment" and period 2]) is interpreted as a net percent change in the outcome. (See chapter 13 in Jeff Wooldridge's "introductory econometrics" for details and examples).