Understanding power requirements for MCU, by example
The first statement is about the power you supply to the board. You could do this at the USB input or at pin 1 of the power header.
The second statement is about pin 4 of the power header, which is an output of the board, not an input. You must not connect loads to this pin that draw more current than the on-board regulator can supply.

To determine the power limit, you will presumably have to dig into the schematics or BOM to find out what the regulator actually is and what other loads are connected to it.

Also, in that same table in section 3.3, there's a column about current requirements that also seems to contradict itself. ...
Which to me tells me the board wants 1A - 2A of current at all times. But then it goes on to say that the USB devices require 0.5A

It's saying that with all peripherals (USB or daughter cards) it might require up to 1 A. If you don't connect peripherals, it will require less, but they don't know what peripherals you will connect, so they recommend using a supply able to provide current to the maximum possible peripheral load.
If you are powering the board from USB, you should design it not to draw more than 500 mA on start-up. Before drawing more current, you must &quot;negotiate&quot; with the USB host for permission to do so (the details of this negotiation process are beyond my knowledge).
They also recommend using a supply that doesn't supply enough current to overload the input protection device.