Why does my car delay shifting?

You would need to have a look at the valve body and solenoids.

Transmission is equipped wit self diagnostic system. Get a scan dnoe to check for trouble codes and if any found, post them here.

No special scanner required but it must be compatible with system. Try a different scanner to see if result is the same.

If you have 2 different code readers not showing anything, I believe there are no trouble codes.

You most probably need to have the valve body serviced.

Just to add to this one when it wont shift unless you let off the gas have the exhaust checked for excessive back pressure.A exhaust shop can do that have it tested when its acting up. Most of the ones I have seen doing that has been a clogged cat. Also do you have a delay or bang into reverse?

When it doesnt shift untill you let off the gas is the car expernicing a loss of power overall?

That whiring sound is most likely going to be a idler pulley bearing or a a/c clutch bearing. You will have to touch a screw driver tip to your a/c compressor and your ear to hear if the noise is coming from the compressor. If its not there I suggest removing the idler pulley and spining it on your finger if the bearing is bad you will be able to hear and feel if its bad.I would have your exhaust back pressure tested at a exhaust shop first. Thats the cheapest easiest thing to check first thats also the first thing I would check if I was working on the car.

Then you could have a bad rear alternator bearing not super common.

If the alternator wasnt putting out enough voltage yes have it tested.