2005 Ford Focus ZX3 dies when gas is not applied

I feel like I've been through it all with this car.  First let me point out that the
check engine light is on due to one of the IMRC control valves being stuck in
the open position. (P2004) It's the only code given.  Aside from that, my car
has begun stalling whenever I take my foot off the gas.  It's as if there is no
idle at all.  It continues constantly for days or weeks, then starts running
smoothly again.  At times I experience what feels like a huge drop in the idle,
some sputtering like it wants to die, then it idles back up when the A/C
compressor kicks in.  Weird?  I think so.  Second issue: I recently replaced
my headlights and one of them doesn't connect well in the wiring socket or
something because it runs the gamut in brightness, from fully on to dim, to
completely unlit.  Interesting tidbit: When my car is running and not dying at
stop lights the light increases in brightness (if dim or not on at all) as I'm
slowing down to make a stop.  I can watch the bright light indicator (which is
lit because the headlight isn't) slowly dim on my dash. Last issue:  My battery
light keeps coming on randomly, without any rhyme or reason.  I've had the
auto shop check the alternator (which was replaced 4 months ago) and the
battery.  Turns out the battery had a dead cell, so replaced it, but the
alternator tested perfect.  Battery light still comes on.  I don't sense any loss
of power or anything wrong when it comes on but it stays lit for 30 seconds to
5 minutes.  If anyone has any insight at all I'd be greatly appreciative!