What a remarkable set of symptoms. For what it’s worth:
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A sound that only happens when the A/C is on pretty much has to be related to the A/C compressor or something else on the same accessory belt.
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A sound that only occurs on sharp turns probably has to do with the power steering or constant-velocity (CV) joints. The power steering pump is probably on the same belt as the A/C.
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A sound that only occurs while braking is probably the brakes (duh). But it could just possibly be a wheel bearing that is stressed when the brakes are applied.
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A sound that is stronger when the brakes are applied but is still present with no brakes sounds like a wheel bearing or some other suspension component.
If I had to guess, I’d say maybe the power steering pump (assuming you have one – which you probably do), but it could be something scarier like a wheel that is getting ready to fall off.
I don’t think I’d take this to a chain. It’s very possibly a complicated problem, and in general those guys seem to have trouble with even simple problems. Your best bet is probably a good independent shop. Or a dealer – who will probably be more expensive – but at least you have a fighting chance of getting a proper diagnosis.