Is it okay to use somebody else’s methodology in my own paper (with proper citations) or is this plagiarism? My research is a content analysis about portrayal of mental illness in films. The research I wanted to base my methodology is also about mental-illness representation. My research questions differ to the other researcher’s questions. We also have different sets of films to analyze.

I really want to know if it is okay if I use the same methodology? Or is it considered plagiarism?
Yes, it's okay to reuse other people's methodology to address an original research question.  It is not okay to copy the methods section of their publication.  You must write your own, in addition to citing them.