I thought information is singular and plural. But now I'm not sure which version is right:
The dialogue shows two important informations.
OR
The dialogue shows two important information.
Which is the right version?
Information is a non-countable noun (you can't have 4 informations), so it is neither singular nor plural. The correct usage is "information" without the 's'. More info here: https://english.stackexchange.com/questions/117552/why-does-information-not-have-a-plural-form
So actually, neither one of your sentences is correct. You can't have two informations; it doesn't make any sense. Maybe you mean "two pieces of information"?
I agree with Kevin; neither version is correct. If you’re not required to use the word “information”, consider
The dialogue shows two important facts.
or some other word. (A somewhat dramatic alternative would be “truths”. Also consider replacing “shows” with “reveals”.)