Should the personal statement include difficult life circumstances you’ve had to overcome? What are the limits on what should be shared?

What you share is a very personal decision. The personal statement provides a chance for you to share what you think will be useful for the admissions committee members to know in order to have a more well-rounded view of who you are, your motivations for pursuing a PhD, and actions taken that align with these values and motivations. However, you should not share anything that you would not feel at ease sharing otherwise.