Serpentine belt

That is strange because they are unrelated.

The power steering works using a pump that has a pulley and is turned by the Serpentine belt. Where you put the fluid, did it look like this?

https://www.carparts.com/power-steering-pump/jeep/grand-cherokee/2003

https://www.google.com/search?q=2003+jeep+grand+cherokee+power+steering+pump

The Brake Master Cylinder has a similar reservoir and also has a brake booster that uses vacuum power from the engine to give you a mechanical advantage. Both are shown here

https://www.ebay.com/b/Brake-Master-Cylinders-Parts-for-Jeep-Grand-Cherokee-for-2003/33566/bn_87327012

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my first thought would be the squealing serpentine belt or could be brake pads. Combining squeal and stall from stopped position maybe you have a bearing going out on something the serpentine belt runs on. example if belt tensioner or A/C clutch bearing going bad could cause drag on serpentine belt. If a bearing is going bad you may be able to hear it under the hood.
https://www.youtube.com/watch?v=AEUe6uKxTv8

if the timing belt brakes the valves cant move so yes if a timing belt brakes it will likely damage your engine. if the serpentine belt brakes you should be alright.

serpentine belts do not stretch as you describe because the tensioner keeps them tight so they just break. It is probably hard and cracking and need s a new one so try that first . The ac has nothing to do with the belt as it will be a low gas problem from leaks and the heat is a coolant problem or a control problem from inside the car.. The grinding sound may be a pulley bearing or some other bearing failing. Why don't you take it to a repair shop to find all the faults so that you can work out how much it is going to cost.

This is the routing of the serpentine belt on the GM 3.8L V6 3800 engine.
It is used in many Buick, Pontiac, Chevrolet and Oldsmobile cars.
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check engine light to come on. " line[number++] = "The anti-lock braking system (ABS) uses several sensors, motors, and a computer in conjunction with the normal braking system. The ABS regulates the brake pressure in order to reduce wheel lock-ups. Reduced wheel lock-ups improve the driver's control of the vehicle during braking. Improved stability and steering enable greater control of the vehicle in the case of an abrupt stop. An ABS warning light means a problem was detected." line[number++] = "The TRAC OFF light or indicator on the dash or message center is usually related to the ABS system, and sometimes to the check engine light. When this is on, the traction system is disabled. A problem in the ABS system is usually the cause, and would have to be scanned for codes. Sometimes an engine problem that causes a check engine light will also cause the TRAC OFF light to come on. In this case, the PCM would have to be scanned for codes." line[number++] = "The security system on todays cars and trucks prevents the vehicle from being stolen. There are many variations of the system going back to the early 1990's. This warning light could be on when the engine is running, indicating a fault has been detected in the system. If left unrepaired, there is a good posiblity that the car will eventually not start." line[number++] = "The tire pressure monitor system in todays cars use a radio frequency (RF) transmitter in each wheel valve stem to relay pressure information to the module. The Service Tire Pressure Monitor System Light means there is a problem in the system, not a low tire. The Low tire pressure warning would come on for a low tire." increment = Math.floor(Math.random() * number); document.write(line[increment]); //--> The anti-lock braking system (ABS) uses several sensors, motors, and a computer in conjunction with the normal braking system. The ABS regulates the brake pressure in order to reduce wheel lock-ups. Reduced wheel lock-ups improve the driver's control of the vehicle during braking. Improved stability and steering enable greater control of the vehicle in the case of an abrupt stop. An ABS warning light means a problem was detected. Warning Lights

This is the routing of the serpentine belt on the GM 3.8L V6 3800 engine.
It is used in many Buick, Pontiac, Chevrolet and Oldsmobile cars.

have a good day !

Fig. Serpentine accessory drive belt routing-3.0L (VIN U) engine


Fig. Serpentine accessory drive belt routing-3.0L (VIN S) engine


Fig. Serpentine accessory drive belt routing-Ford 3.0L (VIN U) engines


Fig. Serpentine accessory drive belt routing-Ford 3.0L (VIN S) engine


Fig. Serpentine accessory drive belt routing-Ford 3.4L SHO engine


Fig. Water pump drive belt routing-Ford 3.4L SHO engine
i wasnt sure what engine you had hope this helps good luck

From what you have described I believe what you have is intermittent belt squeal in the serpentine belt. These tend to squeal in cold and damp weather and usually the noise will typically dissipate once the belt warms up from friction and radiated engine heat. (This is not always the case however).

You should check the belt for age and wear and, if in doubt, replace it as these are quite inexpensive items which need periodic replacement in any event. Also make sure the current belt - and any replacement - is properly aligned on the pulleys.

If you have no record of when the belt was last changed I would replace it even if it looks ok. These are easy and quick for an experienced person to replace.

Often when you replace the serpentine belt the squeal will disappear but return again as the new belt "wears in".

There are some temporary fixes for noisy belts which sometimes work (such as removing it and lightly spraying the belt with "Belt Grip"). There are also 1 or 2 others but I would not recommend them.

There are 2 engines for your Mazda 6, a 2.3 and a 3.0. Below are both diagrams:
2.3


3.0

The serpentine belt has nothing to do with the brakes. It does have something to do with the alternator which charges the battery. the burning smell is probably the result of wasted grooves on the underside of the belt. it is the belt you see just inside the car engine compartment that turns the AC unit compressor pully , the alternator, etc.it is connected to the crankshaft pully.. If you have a front wheel drive it is located on the side of the engine compartment.