What is the typical time between application and contact for a postdoc on Norway?
More than anything, the amount of time is determined by the number of applications. But in general, the hiring process in academia in Norway is much slower than what you're likely to experience elsewhere (at least outside of Scandinavia). To give you an example, I once applied for a postdoc in Norway. Only two people applied, but it still took six weeks before I heard back, and the interview was scheduled fifteen weeks after the application deadline. If you haven't heard anything by the end of June, your application was either unsuccessful, or they didn't manage to sift through the applications before the summer. By that time, I would e-mail the professor you've already been in touch with and ask.
For a postdoc position, I don't think you can count on being informed if your application was unsuccessful, but this might vary by university/department.