How to reference to a whole section of other paper that my paper is heavily based on I have a bit of a dilemma. I am writing a master thesis about a topic that I originally thought was original. It turns out that someone else has done the exact same thing, which forced me to take another perspective on the same topic. Their code and research are old, over 10 years. What I ended up doing is migrating their code to the newest version of the framework used and then evaluating the method in a real-world environment. 

Now I am in a situation where I have to start writing the method section of the thesis report where I describe the method and how the original problem was solved, but I have no real theoretical background/models except for the ones that the authors of the previous articles wrote. How should I reference these things? I still want to show the logical evidence and models that they use without plagiarizing their work. Can I use the same/similar pictures/models/evidences in this section of my report and just refer these things to the original authors and their report? Should I mention it in the beginning of the section that all of the models are from the original authors?
If I understand your question correctly, your problem is that you want to write a section of your thesis and indicate that the entire section paraphrases someone else's article. I would simply add a sentence near the beginning of that section that says something like "The following discussion is taken from Watson and Crick (2016)".

Generally speaking, plagiarism not an issue if you clearly cite the other person's work. Copyright is not an issue if you only use a small bit of their text and you clearly indicate that it's a direct quotation (i.e., using quotation marks or block indentation) and cite the source.

Finally, you might need to worry about whether or not you've done enough new work to merit approval of your thesis, or to merit publication. Your advisor can tell you if you've done enough new work for your thesis. The editor of the journal you want to publish in, or the organiser of the conference you want to present at, will ultimately decide if you've made a contribution worth publication in that particular venue.