The documentation, and API spec both list address3 as a field, however it doesn't seem to display on the front-end. I suspect the field was deprecated on the front-end but maintained in the external API for posterity. Also, the People documentation lists primary address as an attached resource, however it's not recorded as a read-only resource. I haven't had a deep look into the People API yet, but I'm fairly certain there will be other similar resources and attributes attached.
You are correct about the address 3 field. Most address formats use Address 1, Address 2 and then City and State.
The primary address is set from the other addresses, so you can't write directly to it. You can read how the primary address is determined here - https://nationbuilder.com/edit_primary_address#automatic