As far as the brakes go...a good practice is to always give the slider rails a good cleaning and replace the hardware
(slider pins or boots and bolts ) lube the caliper slide rails with brake lube. Also as mention by someone else a wheel bearing is suspect based on your condition...Brake pulse (bearing not running true) which could also be the cause of your brake pulsating. You could try 2 small checks..Lift the car off the ground and brace something like a pointer on a solid object very close to the tire and hand spin the wheel and look for any runout, then also do the same test with the wheels removed against the rotors you might find some wobble that way. In any case a sticking caliper or wheel bearing is my guess based on what you describe.
