Is there a website where I can access the complete and most recently updated version of the United States NEC for free?
Yes, the NEC. Is free once adopted . search for free NEC and you will find it. This is only for the "code" I don't think they release the hand book that has a lot of information on why, this is the version most inspectors use , but once adopted the NEC is free on line. Just checked look up nfpa.org free access just need to sign in..
The City of Tool, TX, USA, has provided a freely downloadable and fully searchable PDF of the NEC 2017 , currently (April 2020) in effect in most US states , to be accessed without the need to create an account. I assume they have a license.
 https://www.tooltexas.org/departments/building-code/ (approx 7MB)