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the only way to know is to scan the ABS system for faults. you have a speed sensor on each wheel, one of them is likely faulty. It is a couple hours of diagnosis and repair.
Sure- check your fluid level to make sure that isn't a cause of the problem (ABS light being on typically means an electrical faults in the system) and the mechanical brakes will work fine- you just won't get ABS activation, so don't slam on the brakes on ice or sand, or follow too close to react.