Jack plug is perfectly valid. If you want to get technical, a jack is what you use to lift cars, what he's holding is a TRS connector (Tip-Ring-Sleeve, for the three parts of a stereo jack, the most common form of the TRS), that connects to a socket. From what I've seen, professionals usually call the socket a socket, and the plug simply a jack.
As for charging, it's only a question of voltage and amperage you send through the jack. As long as it's below the socket limits (ie. the plug doesn't spot-weld to the socket contacts), you can do pretty much anything. Certain electronic synthesizers use the mike input to accept a specially crafted audio file that carries firmware updates, and I've seen magnetic stripe spoofers that use similar audio files played back from a smartphone to simulate a card to the reader.