couple of problems...

[kaze]

1. I have a '97, 2.2l (85,000 miles) Cavalier. No major problems since I got it, but the engine started being noisy in a cold weather while accelerating or driving up the hill, two years ago. That problem kept progressing over the time (more noise just after start, less power when I accelerate). In a very cold weather (I'm in Canada :-)) it would happen that after start (always without problem), when I make the first stop (intersection), it stalls after that for a moment (engine roaring, but moving slow for a minute or less).
My mechanic used to tell me that was normal for the Cavalier ('why do you drive that thing?'). Now he tells me: "That engine's getting noisy. You might want to sell it." Now it's summer and it runs fine (a little bit louder than before), but I believe that it is going to be worse next winter.
I’ve changed spark-plugs, tried with different injector cleaners, higher octane fuel...didn't help.
Should I follow my mechanic's advices, or there is something I can do?

2. The second problem: Whenever I press the brake pedal a squeaky sound can be heard for a moment, coming from (I believe) rear brakes. No difference in brake performance, or noise while actually breaking. At the beginning I thought it was coming from the pedal, then I realized the noise originated from the back of the car.

I apologize to everybody for my obvious lack of basic automotive knowledge, but if there's anyone out there who can help me with an answer, I will appreciate that.

[GTP Dad]

Try using a synthetic oil in your car. If you are using a mineral based oil it may not be free flowing enough to keep everything lubricated in the cold temps this should help keep the noise under control since synthetics flow better in cold temperatures.
For the stalling problem check to see that you have a new fuel filter and keep a bottle of dry gas, use the isopropyl type in your fuel tank at all times. Water can cause stalling and surging problems and can cause fuel filters to block up and restrict flow.

[GTP Dad]

As for your brake problem, you may need to put some brake lube on the area behind the return springs inside the drums. Often times these will get dry and cause a slight squeek or noise. To do this remove the brake drum, lift the spring slightly and put the grease on the backing plate just behind the springs. Be very careful not to get any grease on the drum or the brake shoes as this will cause a lot of problems, also go to the autoparts store and get special brake grease, DO NOT use regular grease for this.
If you have disc brakes in the rear you may only need to wash the brakes out with a high pressure hose as dust may have accumulated between the pads. Hope this helps!

[public]

You won't need synthetic oil. It is expensive and does not flow any better in the cold. Cars were quiet in the cold for years before syntheic was invented. Syntheics are better if you can afford it, but that relates to uniform molecule size which means less (zero) volitales. If you had used syntheic since new it may have helpped. You may need a lower viscosity (lower number=better flowing) if that is your problem. It certainly wont hurt.

These engines are prone to two problems that make them noisey. I have an 89 and a 94 so I've been there with this noise collection. One is rapid ticking cause by the valve train. Check the clearance on your rocker arms. They become worn and sometimes loose over time. The other is the belt tensioner, check and oil the spring(behind a cover). Just shoot some oil in through the plastic seal around the edge.

The stalling may be a sticky IAC valve. This is common on these cars. Remove it, clean with carb cleaner and a toothbrush, clean the hole the same way. Try not to move the pintle in or out while doing this.

Sounds like the brake issue has been covered.