No, the Mojo, and all Chord DACs, are single ended. There is no benefit to plugging the separate headphone jacks to your stereo. Even the RCA output measures better, except for Voltage output, than the XLR output (which is derived from the SE out) in the Hugo TT and DAVE.
As for your connection to the phone, you are likely hearing cellular interference and/or a loose connection with the USB cable in the Mojo input. Unfortunately this loose connection can happen with some USB connectors.
As for charging, yes, you would connect to both the USB ports to charge and listen at the same time. The fact that it takes a long time to charge is not surprising as PC USB ports are not high current ports, especially when you are drawing power while listening. Try using a sperate 2A 5V USB charger plugged in to the wall instead. Often times manufacturers may overstate their charger specs, so even though the charger is rated at 1A output they may not quite deliver that amount of current.