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A leaking intake manifold gasket is very common on this engine. The way I find it is to get a water bottle and spray a stream of water around the intake runners where they attach to the head. They normally leak at the ends,, near the #1 or #6 cylinder intake runner. If the gasket is leaking, the engine will stumble when the water is drawn into the cylinder from the vacuum leak.
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Because there is a fault in the air bag system. Get it looked at by a shoop to determine why.
There can be few reasons the power is not getting to the compressor. Low pressure switch, a/c switch, or any other part of the electrical circuit that powers the compressor. It's best to have a wiring diagram and a good understanding of the requirements needed to engage the compressor.
You will want to get the charging system checked to see why the battery isn't charging.
The engine oil will not cause water pump failure.
This kind of advice is best given after a visual inspection to determine what needs to be done. You may be able to repair i or it may need to be replaced.
If your check engine light is on, the engine may be keeping the fan on, is the light on?
Check all the battery cables, make sure they are good. Here is some info on how to properly check a starter: http://www.excelauto.com/online/Tech.d/strvdt.html
It is quite possible the alternator, but it is best to have this inspected by a shop, and not the one you took it to, because they obviously didn't check it properly, or they would've found the problem. Have a starting and charging system check performed to identify the issue, have it done by a reputable shop, and use only quality parts. Using the least expensive shop and or parts will cost you more in time and money in the long run.