Car dies/ transmission flutter

I'm having several issues with my 2004 pontiac
grand prix. I'm not sure if the issues are related or
not. The first thing is that when im driving at
anything above 50 mph there is occasionally a little
glitch when the car shifts. If it were shifting up it
feels like it goes down and then back up.
Sometimes its more than occasionally and it will
do this several times in a row. The second problem
is that sometimes it will die right after it starts. I
will restart it and give it a little gas and then it will
usually stay running. Sometimes it dies a couple
times. The most recent problem is when I started it
this morning the idle revved up all the way to 4000
rpms and the lights were flashing on and off
(headlights).  I have replaced the spark plugs, put
in a new fuel filter, had a fuel cleanse, and put in
some injector cleaner. I was going to have a new
fuel pump put in, but my mechanic said he thought
it was fine. Any advice would be appreciated.
Thanks in advance