2003 Dodge GC 3.8L Where can I find a replacement cowl silencer pad that goes between the engine & firewall

Brake pad wear warning sensor scrapes only when brakes are not applied. Replace pads

Could be water trapped somewhere in the cowl due to a blocked drain hose.

No one ever said new means good. Try another thermostat. Make sure it is the recommended temp for the vehicle. I would spend the extra money to buy a dealer thermostat. What controls temp is restriction of flow thru the system until a set temperature is reached and the thermostat opens. Has to be a thermostat.

If your engine reaches normal operating temperature then it sounds like the heater valve is not operating. Find the valve on the engine firewall passenger side and manually open the valve. Find it by following the 3/4 inch heater hose to the firewall where it is connected to the valve. Most likely the cable ( or vaccum hose)from the temperature dial to the valve needs replacing.

Your drain tube for the air conditioning is plugged up, and instead of draining on the ground, it's leaking on the carpet. You need to go under the car and locate the tube (it's on the passenger side, in front of and below where the front passengers feet would be. You will need a long thin wire to clean out the blockage.

The pump is located on the passenger side of the engine compartment, back by the firewall. Look in the middle of the firewall by the cowl and you'll see a small plastic line going into the cowl. follow it back and you will come to a T fitting. Follow it to the passenger side and it will go into the Vacuum pump that controls the Cruise control.If you follow it to the other side, it goes under the Battery box. this is where the Servo for the cruise is located. Check the lines for small cracks, wear spots or even breaks. The plastic line can get beaten up pretty easily.
The easy way to see if it is your vacuum pump, turn the key on and listen. you will hear 2 distinct sounds. The first sound will stop in about 15 - 20 seconds. (fuel pump?) the second sound is the vacuum pump. If it turns off in 45 seconds to a minute (or slightly longer) the vacuum pump is probably ok, as are the plastic lines. The sound of the pump stopping means that vacuum has been achieved and is holding vacuum. If it keeps running, the pump is bad or the lines have a break in them. If the lines have had a hole in them for a long time, the diaphragm in the pump will have gone south. This is not a servicable part and the pump will have to be replaced. The pump is available from a dodge dealer but most likely the parts guy will not have a clue as there is no picture in their manual and a very poor description. When talking to them ask for a "03 Ram 2500 CUMMINS Cruise vacuum pump"
The part costs $212.70

should start on the pass side of the intake and go to a fitting on the firewall which goes under the cowling and through the cab.

I have the same problem on a 2003 Town & Country. The cover for the front 3 cylinders is quite straight forward, but in order to do the rear cylinders I believe you are going to have to remove the cowling below the windshield. You will need a gear puller to remover the windshield wipers first, then remove the cowling. Than should give you more room to work. It's still not going to be easy, but it sure beats paying hundreds of $$$$ in labor charges.

Had similar problem with 2003 Dodge GC. Replaced the parts you mention + rack & pinion, then to fix the now noticable whining noise, replaced power steering pump and pulley. Fortunately was under an extended warrentee at 46k miles.