2007 Equinox stalls/shuts off

I apologize in advance - I am not car savy but will do my best to explain the problems I am having. (I'm one of those people that brings her car in for a problem and has to immitate noises because I can't verbally explain the problem.)
Hopefully this will make some sense to you.

My 2007 chevy equinox began having [new] problems last year. Currently over 50k, but was well under 50k when problems started.

When first started in the morning, the engine seems to run fast. The needle on the gear display (not sure what it called. The dial display to the right of the speed dial that tells you what gear you're in)starts off between 1 and 2. After letting it run a few minutes, the engine seemed to calm/slow down a bit, and the needle would drop below the "1." However, even then this needle seemed to "bounce" and the engine felt & sounded as though it were kicking or revving. The "bouncing" of the needle became increasingly prominent as time went on.

When I put the car in reverse to pull out of my parking spot, the engine would "kick" and the car would ****. This also happened when I put the car into drive.

I would notice the same kicking and jerking as the car moved forward if I let it roll by taking foot off the gas and break. Once I began driving it for the day, it seemed to get better, but would recur again in the morning.

At the same time, I noticed a delay when the car shifted gears when driving. The car seemed to "pause" before shifting gears at higher speeds - usually on parkways. I wold also notice a weird "pause" between taking my foot off the break and acellerating - it felt as if the car was about to shut off or stall.

Eventually the car flat out stalled - actually the car shut off completely. I was backing up out of my spot one morning and everything just turned off. It was very frightening.

I was able to get the car to the dealer, who gave me a few reasons as to what was wrong.
Reasons allegedly included: (1) The problem occured because I used regular gas (yet there is no requirement to use super or better - this was one of the reasons I purchased this car instead of a nicer brand.) (2) The engine needed "cleaning" (3) Faulty mass air flow control filter.

A few hundred dollars later, even though the car was under warranty, the dealer said these problems were not engine/power train problems that would be covered by the warranty.

**Not even a year later, the probem has returned. I called and asked the dealer what the diagosis was last time (since it seems to be the same problem) and was told "faulty mass air control filter" (?)

Prior to this I had several other issues with the car (1) when I originally picked the car up (purchased new) the alarm and auto start were not installed, and I had to bring it to the dealer to be installed. (2) stabilitrack light would turn on randomly (indicating stabilitrack had been turned off) and say it needed service (3)engine light would go on randomly (4)if I drove through a puddle OR if it rained, upon acellerating the engine would sometimes sound like a boat rudder under warter [repeated complaints to dealer - no one has been able to diagnose or explain the problem] Going though a puddle also does something to the stabilitrack and when this happens I feel as though I have no control over the car (5) windshield wipers get quirky/dont work WHEN IT RAINS (5)front window defroster seems to have no effect when cold out(6)when cold out, alert light goes off telling me to check tire pressure & tire pressure seems to change througout the day (7)bolt on rear hatch unscrewed and hatch would "pop" when opened - bolt was tightened by dealer but now door is off alignment and the top right corner scrapes against the body of the car as hatch reaches max height.

Also, the engine (or something in it - a fan?) Continues to run after I shut and exit the car.

My biggest concern now is the stalling/turning off. I included the rest because maybe its somehow releated?

Thanks in advance for any advice you may have.