When opening someone else's document, is there a way to tell InDesign to use your preferences? As an example, I have my settings set to increase/decrease the leading and kerning in 1pt increments. When I open a document created by someone else, the document uses their settings instead of mine. Is there a way to tell InDesign to use my custom settings instead of the document's settings?
No, at least not for settings which are document-level rather than application-level. Those settings are saved as part of the file.