With a whirring noise possibly indication a faulty bearing, just because it isn't loose doesn't mean it isn't bad.
For the brakes, yes the calipers may be be hanging up. More commonly the pads get stuck in the guides or the sliders get sticky from negligence. Either way, if there was an overheat condition, I'm willing to bet the rotors aren't ok. I'd replace those too. Besides, whenever replacing brake parts, always replace rotors/pad and drums/shoes together, or at minimum replace the pads/shoes and have the rotors/drums machined so you have a new surface.
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