My personal belief is that the contacts in the stupid microUSB connectors get oxidized and cause the "low power" warning. I've sort of proved this by taking an old Express and soldering wires directly to the circuit board and a USB power adapter. I haven't had the warning since. Before I did that, I could sometimes swap out the USB cable and get rid of the warning. If you have the USB cable with the embedded Wi-Fi module then that's not so easy/cheap to do. Try spraying some electronics cleaner into the microUSB connectors.
As for the remote problem, I don't have any good suggestions. I don't think it's related, but cleaning all of the connections can't hurt.
