When I turn on the air conditioner after a few seconds it starts making a horrible noise....it works when the noise is not there, but once the noise starts the it doesn't blow as strong.

I would check the cylinder compressions, sounds like you've already caused more damage, so a little more horrible noise won't matter

the rpms drop because you are adding more of a load to it. it should level out after a few seconds.

start with a new belt first...could be the clutch try spraying some wd 40 around the pulley and see if noise goes away.

I do not think that the battery change and the noise for the a/c is related, probably just a coincidence.

If the a/c makes a loud noise when it is turned up, I would try switching to vent to see if the noise is still there. If it is, then it is the ventilation fan likely located on the firewall or under the dash under some plastic paneling.

There is no reset button for the a/c.

Good luck on this repair.

remove the AC relay to shut the AC off all the time. Not sure why it wont start but you may havea security lockout. Fully charge the battery to proceed.

your description sounds like the gears inside the the same differential you just replaced.

Hello, It sounds like your hot/cold blend door actuator is either hanging up at times or it's loosing it's calibration range because it's starting to go bad. The ticking noise is most likely the actuator trying to close off the hot air port but is unable to stay closed allowing hot air to mix with the cold. If it's just a weak blend door actuator, it will act up more when the air is on full because it has more resistance due to air flow. If possible try to see if the times it acts up decreases when you start the A/C with low fan speed.

there is a mode controller/actuator in the passenger side area(behing glove box) that will make clicking and rattling noise when failed but I cant say it makes a "horrible" rattle but it is quite audible clicking and clearly is a noise coming from inside the left dash area

Afterrmarket compressors are cheaper. Call around.

Sounds to me like you need the alternator idler pulley. Look at it and see if it has a big washer covering portion of the pulley, or if the washer is inside the pulley. If its inside, than you have an old pulley. Replace it with the one, that has the big washer in the middle of pulley. You do have another idler for the A/C compressor. Those I have seen fail also. But 80% of the time its the alternator idler pulley.