Does the PII collected change depending on whether you’re an adult or a child?
No. No one under 13 is able to use Foursquare.
Can you correct or update your Personally Identifiable Information (PII) if you want to? Does the site tell you how to do this?
Sort of. Your password, phone, email can be updated through user settings page.
If you’re a child, can you sign up with adult consent?
No. The service isn’t available to anyone under 13.