something in the charging system???

Not sure of the GT/SE model thing but it's a 4 cylinder.  That should help.  I did last
week have a backyard mechanic change the front brakes and add transmission fluid not
sure if something could go wrong with that?

Earlier today the battery light came on.  The lights dim, and the cigarette phone charger
won't work.  Then the heater bogged down, so we turned off all accessories.  The airbag
light came on.  Then the car jumped, accelerating itself followed by the engine bogging
down.  Laying into and off the gas pedal is minimally responsive with an increase in
RPMs.  Usually the car runs at 2 RMPs but while this is happening the RPMs are
between 5-6 and the speed isn't really there.  The temp stays normal at the halfway
point the entire time though.  The first time this happened we were able to drive 70
miles and it simply cleared up.  Then the second time we were able to only drive about
44 miles and then I noticed my window wouldn't go up followed quickly by the car being
dead alongside the road.  I waited about 10 minutes or so and then the car fired up.  
After the first time this happened the car ran for about 50 miles prior to the battery light
coming on.  After the second time, again, after the car had died alongside the roadway,
while warming up the car the battery light came on.  Whatever is wrong is getting
excessively worse and quickly.  I'm worried about being broke down in a remote area
without cellphone service and in all ways being stuck.  This can lead to a deadly
situation given the extreme cold.  What are somethings that could cause a situation
like this.  The battery checks out fine.  The alternator checks out fine too.     

Also, during the second time the car was jerky when I stepped on the brakes.