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Tightening the belts my help. Battery gauges fluctuate my show bad diode in alternator or check the skinny wire going to alternator. Sometime get corroded and do not have good contact. Servicing transmition my help.
Water pump noise - need to change. About the AutoZone - you are right. I do not trust them.

 

also check the EGR too. it could be gunked up or have corrosion/.

 

no codes since you started working on it?????????????????????????

 

try replacing your serp belt. I had the most annoying chirp coming from the engine. I had changed the belt, the noise continued... I thought it was either the idler pulley or water pump. I replaced the idler and the noise continued. the H20 pump is only 1 year old so I was having a hard time believing it was bad. then I wondered if the harmonic balancer was worn and not tracking true. I ended up having a local shop look at it. turns out the "new" belt I bought was bad. replaced it again and problems went away. that won't fix your tranny problems, but if it's not charging odds are the belt is slipping and thats why.(providing the alt is good)

 

What year is the vehicle? Auto or Stick? If you have an auto with electronics, you may have something as simple as a bad battery. Auto Zone said it was bad, your voltage guage is fluctuating, there may not be enough juice to work on all the electronics. I've got a 94 GT mustang that I haven't driven in almost a year. I turn the engine over and go around the block every once in a while, but when the battery could no longer hold a proper charge, it would die on me when I put it in gear. (Tranny with electronics) Got a new battery and now it's just fine. My 2 cents.

PS: I should confess that I have a great uncle who was a Vietnam era Army Mechanic and Ford tech for a long time after that, always tells me to look for the simplest solution first.