I am self-studying pre-socratic philosophy. I want to know what are the relevant questions that I need to ask to myself. The idea is to ensure that I understood the important parts of this period in order to have a solid basis to understand what comes next.
Jacob N. Graham provides this introduction to Presocratic thought:
Presocratic thought marks a decisive turn away from mythological accounts towards rational explanations of the cosmos. Indeed, some Presocratics openly criticize and ridicule traditional Greek mythology, while others simply explain the world and its causes in material terms. This is not to say that the Presocratics abandoned belief in gods or things sacred, but there is a definite turn away from attributing causes of material events to gods, and at times a refiguring of theology altogether. The foundation of Presocratic thought is the preference and esteem given to rational thought over mythologizing. This movement towards rationality and argumentation would pave the way for the course of Western thought.
He also describes particular Presocratics in detail. This, or similar surveys, might be a place to start in one's own investigations.
Based on Graham's account a question to ask oneself is how the Presocratics attempted to describe the world in non-mythological terms.
Graham, J. N. Ancient Greek Philosophy. Retrieved on May 7, 2019 from Internet Encyclopedia of Philosophy at https://www.iep.utm.edu/greekphi/#H1