the vibrating in the steering under braking suggests a warped brake rotor, and the sticking sounds like the caliper may need to be rebuilt or replaced with a rebuilt caliper because the piston is sticking. you can buy rebuilt calipers from autozone pretty cheap, it is not that hard a job if you've done this kind of thing before and know how to bleed brakes.

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2005 Mercedes C230k sport sedan, 6 speed
1987 Porsche 924S - 968-engined track car