So we have a 2002 Pontiac Sunfire, 2.2 litre.

Bought the car, used it not even 24 hours later the battery light came on, did a multimeter test, showed the alternator was bad, bought a new one and changed. Worked good for approx a week. Now the battery light comes on and off.
When the battery light is on, the wipers are slow, the stereo quits working, when idling the rpm's will drop down and before stalling jump back up, all the lights on the dash will light up (battery, abs, e-brake, airbag etc.), the speedometer and tachometer will quit working also.

ANY IDEA WHAT THIS COULD BE???

possible poor wiring connection or loose wire. There is a fusible link that all power from the alternator must pass thru on its way back to the battery. its located on the starter solenoid

Start by testing main power and ground wiring for the charging system.

Start the engine and turn on all electrical loads, A/c, headlamps, rear defrost etc.
set your dvom to volts
put the dvom red wiring lead on the + bat terminal and the black lead on the large wire on the alternator. A good reading will be no more than 0.4 volts any higher and you have high resistance on this circuit. possibly that fusible link?

test the ground circuit by:
will car still running as per previous test
dvom black lead to the neg bat post and red dvom lead to the alternator outer case.
the reading should be 0.2volts or less. If higher the ground side circuit has high resistance

Had a issue that was like this in a honda i had,Seems the re-man alt that I bought had a bad voltage regulator..And when that happened it also caused a battery issue,If i were you i would get a new alt and battery for your car,Also check your wiring..

I had this exact same problem, when all the dash warning lights come on, speedo & tach & gas gage + temp gage, none of them worked...It was a grounding problem that has happened to me twice...Once, it was where the main grounding block area is, between the engine block & trans, where the PCM wire harness grounds too and also a couple of other harnesses share the same grounding point, and there is a stud that these wire harnesses go on...I had some corrosion between the PCM ring terminals that was causing a short to ground. The second time it happened, it was the battery ground wire that comes from the same location where those other wires are all looped to the same ground, I call it a battery ground because it goes to the battery tray on the other end, it was a little loose at the battery tray + had some corrosion, I tightened it and just to be safe because this happens every now & then, I installed an extra supplementary battery tray ground wire and attached it on one end the same spot, and the other end to a different hole attachment point...The reason why I did it that way is so the least path of resistance will be travelled, and I figured it'd be a guaranteed good ground...And it is, problem solved..Dash gages work fine, headlights are brighter, power windows don't slow down & stop anymore..

check your grounds.... sounds like a bad ground.