If I booked my ticket to Chicago from Colorado with my passport, do I need to show my passport in order to get my ticket and board the plane? I only have my drivers license with me. I'm not a us citizen but I am a permanent residence.
You don't need a passport to "book" a domestic ticket so I don't know how you used your passport to "book" your ticket. Yes, you can fly that flight with just a US drivers licence. You can check in online.
I am flying from the US (US citizen) to Santiago and then to Punta Arenas the next day. Will I be going through Customs and Security for the 2nd day "domestic flight ?
There is no Customs when traveling on domestic flights. You will likely have to go through security before your flight to Punta Arenas. Also, be aware that there are numerous cities in the world named Santiago, so be more specific when you're discussing one.