RCAs

The way you have it hooked up now is one channel from the head unit to the amp, splitting to two channels at the amp.  The amp is getting one signal (one channel) instead of two. 

I can't think of any harm coming out of this, but to answer your second question, yes, the sub is playing only half the recorded music.  Although sub frequencies in stereo can't be located, there is a distinction in the recording of what sounds go to which channel.  Some recordings are noticeable if a channel is missing in the low frequencies, others are not.

You'll probably see a big difference when the HU problem is solved.  You can tell if it's the cables by just reversing them.  You know the red one works, so plug it into the left jack to troubleshoot.