When I said it is wireless, it has power and ground, but communicates wireless to the RFH. From the service info.
In the Passive Entry Keyless Go (PEKG) system the doors are unlocked passively; however, they must still be locked actively after exiting the vehicle using the tactile Lock button on either front door Smart handle. When the system senses a hand approaching the capacitive switch in the door Smart handle pull, it sends out challenge messages through the Low Frequency (LF) antennas to authenticate the presence and location of a valid FOB with Integrated Key (FOBIK).
The FOBIK responds by sending a Very High Frequency (VHF) message back to the receiver within the Radio Frequency Hub Module (RFHM) (also known as the RF Hub). If the RFHM determines the FOBIK is valid and that it is located outside the vehicle in the same zone or vicinity as the door handle or deck lid switch being activated, it sends an electronic Unlock Request message over the Controller Area Network (CAN) data bus to the Body Control Module (BCM) to automatically unlock and allow entry to that aperture.
As far as how far you can go with key out, until you run out of fuel, or shut it off, whichever occurs first. That is if you can stand the dinging. For safety the vehicle will never shut off.