Ok, Here is the deal.
What this place probably didn't do when they replace the brakes is put what is call Anti-Squeal on the backs of the new pads. What this is is a rubbery coating to prevent the squeal. Some times with a new brake job such as you had done the pad and rotor create a vibration that sounds like a squeal or some call a squeak.
The Caliper doesn't sqeak or squeal on its own it is a combination of both that creates the squeal or squeak. Which is a vibration.
As far as the brake caliper if a caliper goes bad or locks up you will only loose braking at the wheel that the caliper has malfunctioned at. You will not loose all your braking.
Now addressing the sticking caliper. I would suggest and if the garage you are going to are on the ball they will recommend replacing both calipers. And I suggest that you do. If they don't say anything about replacing them both mention it to them and see what they say.
Hope this clarifies things. If not don't hesitate to keep asking?'S until you understand.
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Wednesday, July 2nd, 2008 AT 9:10 PM