I have AC carrier brand outside compressor. The cable connection from the unit to the
Power shutoff box and the shutoff box itself have all been rusted.
I took the electrical shutoff box apart to see how it was wired and see if I can
Replace it. That's when I notice something that I thought should be against code.

Here is what I saw: the thermostat wire (18 gauge) from the AC unit inside the house was
Brought into the shutoff box outside of the house, and then fished into a single whip cable
Along with the 240v wires (red, black, white, all 8 gauge) and brought into the compressor.
This sounds dangerous mixing low voltage (24v) with high voltage (240v) cable in the same whip. I checked out other compressor's wiring in our neighborhood and only saw
One whip going from the shutoff box into the compressor, which tells me their
Thermostat wire must be wired similar to my unit.

Is this how the pros wire the compressor, all the wires to the compressor in one whip?

It is pretty common to see that practice on older systems, but isn't a good idea,the thermostat wire doesn't need to be in a conduit,strap it along the lineset and call it good.

That type of wiring has been against the NEC code for years. Hvacservicetech07 has the right idea but check to make sure the wire you use for the exposed low voltage line is outdoor grade UV protected and that is what is calls for today. I believe Home Depot/Lowes has that in stock at least in our local stores they do. Since your job will probably not be inspected since it is a repair you can get by with the regular T-Stat cable. It will last for quiet a few years before the outer jacket goes bad.

Since the thermostat wiring is all done through our unfinished basement and attic,
I can rewire the whole thing with the UV protected cable. It's better to do it correctly now
Since I am finishing the basement putting up drywall.

A couple of questions:

Question: Do you have any pictures I can look at on how it should be properly done?

I said earlier, the old T-stat wire was going from the house to the outside
Shutoff box, then through the whip to the unit, and that's my next question on how
To wire this:

Question: Where should I bring the T-stat wire from the house into the compressor?
I rather not making too much holes on the exterior wall and cause future water leaks
(almost all exterior wall holes in our house done by the builder had water leaks, which
I have fixed with a generous amount of 100% GE silicon II).
May I bring the T-stat wire from inside to outside along side of the compressor's copper
Pipes then tape or zip tie it? The 3/4" copper pipe is insulated with rubber pipe insulation.

By the way, the UV has damaged the rubber pipe insulation. It doesn't feel soft
Any more, and it becomes almost a dust of black particles when touched. Is there
A UV rubber pipe insulation you would recommend? Is there a better solution?

Thanks for all your help

May I bring the T-stat wire from inside to outside along side of the compressor's copper
pipes then tape or zip tie it? The 3/4" copper pipe is insulated with rubber pipe insulation.

That will work fine

By the way, the UV has damaged the rubber pipe insulation. It doesn't feel soft
any more, and it becomes almost a dust of black particles when touched. Is there
a UV rubber pipe insulation you would recommend? Is there a better solution?

Unless you want to replace the pipe insulation I would leave it alone and just run the wire. If you want to replace it then a trip to a local Home depot or better yet a HVAC supply house would be in order.

Running the wire along side the refrigerant lines will work.