I’ve been charging at a Windows computer via a USB2.0 port using the data cable that shipped with my old Samsung Galaxy. I had many of the same problems described here (CPU very hot, lightning bolt and LED flickering, phone not really charging), but I wasn’t experiencing problems with rebooting or functionality.
My incredibly lo-tech solution was to plug the cable into the phone, put it down, THEN plug the cable into the computer. It then started charging happily, but it goes wrong when I move the phone, until I repeat the process described above.
This strongly suggests to me that my issue is with the connection. I’m going to test with another charger when I get home to see if the issue is with the cable or the phone. Given that this cable worked perfectly with my old phone, I suspect it’s the FP2 (unfortunately!).