What kind of citing permission do I need for a research project (not a master thesis) report that I am writing?
I think you are mixing two issues up with each other: Copyright and Referencing/Citing sources. The first one is a primarily legal topic whereas the other one comes from scientific integrity and proper work.

Copyright prevents you from directly using material without permission. For example, I cannot simply take an arbitrary figure from another paper or the Internet and publish it in my own paper. Therefore I need to get permission to reuse such a figure in a publication. But mostly not for personal use and stuff which will not get published or spread around.

Referencing and Citing is required in science. This means that you have to give the source of any ideas, equations, figures, ...  which you have not developed and created on your own. Even if you were allowed to reuse material from another paper, you still have to cite it correctly.

For your research project, you should talk to your supervisor. Since it does not get published I assume this is far less critical from a copyright point of view. For example, if I collect information for an internal summary on a topic, e.g., by summarizing the work of other researchers, I do not obtain a permission for these figures since this is way over the top and takes away to much time and resources. Copyright is most important if you want to publish your work. I do not think that your research project requires this, but talk to your supervisor.

Nevertheless, you WILL have to cite all your sources correctly independently from how you decide to handle the copyright.