I spelled my middle name wrong in my application.

I have a middle name that is shortened in my official documents (green card, transcripts,passports, etc.) even though my parents call me by my extended middle name. I didn’t know (until now) that I had used the extended middle name instead of the official in my Common App (although not in my UC app because UC only asked for the first initial). How will this impact my decision if they look at my official documents (my green card and transcript)?

I would not worry, although you might let your GC know. That is probably where they will start if they have questions.