my wife is student and i am accompanying her, we have a schengen visa type D for 90 days from Germany embassy. we are iranian.
because her study takes longer we have to apply for a resident permit from germany.
my question is: can we travel in other schengen countries after we have the residency permit? or because we have a 90 day schengen, we can only travel only in my first 90 days ?
Once you have your residency permit you are allowed to travel freely to any country in the Schengen zone. this was the case for my Russian friend once she got her French residency permit, so I'm pretty sure the same applies to Germany
You will be able to travel freely within Schengen zone with your first 90day visa as well as with your residence permit. See:
When you already have the residence permit, you can stay in any other Schengen country for up to 90 days at one time.
This might be a helpful site for the residence permit application:
Enjoy your stay in Germany!