Answer for Noise when Accelerating...

I will answer the last posted problem first, and that is the issue of the scream upon starting sometimes. You diagnosed it correctly.  But I do recommend that you replace the belts at this time.  The slipping belt is probably the alternator belt but I always try to replace all the belts at the same time to establish a time frame. I recommend cleaning the grooves in the pulleys with a wire brush and some aerosol parts cleaner.  Blowing them out with compressed air would also help.  One problem is that only installing a new belt without cleaning the groves would not allow the belt to fully seat in the pulleys, thus causing shorter belt life.

Now on to the engine having problem while going up a hill,  Assuming that the engine is in good tune, spark plugs of the heat range recommended by the manufacture and properly torqued in the cylinder head.  Threads should have an antisieze chemical brushed on them to prevent them from getting stuck in the head. Has the fuel filter been
replaced?  Remember the fuel filter filters more fuel then the engine consumes and returns the unused amount back to the fuel tank, so it filters many hundreds of gallons of fuel every time the car is driven.  Your car may be suffering from fuel starvation as it requires the most amount of fuel when going uphill.  It also could be a buildup of carbon in the combustion chamber that is causing a premature ignition. Last thing I will talk about is the catalytic converter.  A clogged converter will cause lack of power at high engine speeds and a noise coming from the intake system is usually the air cleaner air intake area.  It can still pass the smog test with this condition.  So my recommendation is this, start with some chemicals.  Add at separate times according to the direction on the product.  First I would add a fuel injection cleaner to the fuel tank and give it time to work. This will help clean the fuel delivery system as well as decarbon the combustion chamber.  I would do this two times using a full tank of gas each time.  Then if there is not a change, I would use a product to clean the converter.  The products that I use are:  Sea Foam motor treatment (www.seafoamsales.com) and CRC GUARANTEED TO PASS Emission Test Formula (www.crcindustries.com). Remember this is assuming that your mechanical parts of the engine is maintained and properly tuned.