My ABS brake light is on and the right front tire feels like its jumping.

Abs detects each wheel of the rotation.i will check from the tire then monitor with the scanner to see the abs sensor on each wheel and chk any fault code as well.anyone of the abs sensor have not detect correctly,it will be not working right.that's the basic of ABS.good luck

have tires checked and rebalanced --if rotors were cut have rechecked if new than need to check the cv axles one of the axles possible going bad-- also steering components worn or loose --also bad shock or ball joints

sounds like you have a abs sensor failing to read a signal on one wheel , car thinks that the wheel has locked up and as you press the brake it cuts the abs in and tries to release the brakes which is the noise your hearing and poss pulling to one side as you brake untill computer recognises a fault and shuts down the abs system which is when the abs light comes on, this pulling may indicate which one is faulty, it will need a abs sensor or signal ring on the drive shaft,usually a front one ! a damaged wheel bearing can cause an interupted signal to that sensor, failing that your abs pump is faulty, hopefully not the pump as this is very expensive

sounds like you need new ball joints. jack the front of the car up one side at a time so that the tire is clearly off the ground. once you do that try to push and pull the tire from left to right. if it does move then its your ball joints.

The grinding noise has alot to do with worn pad's and rotor's(the disc),and if those two part's are worn down enough ,of course your going to feel like your not going to stop.Have those replaced and your brake lines checked(and/ or bleed) out to make sure there aren't any leak's and the master cylinder .

the problem your having is most definatly abs. The speed rings on the hub at times can get a hair line crack, this causes intermitten issues like your discussing. Since you noted right pull? Thats the ring i would have checked first

The noise is normal ( somewhat) Things that can make it happen too often are mis adjusted tire pressure. wrong tires ( all the tires have to be the same size) worn out tires low grip. The ABS system will work normally only if a tire is trying to skid. if the seed senser dectects a tire is going the wrong speed conpared to the others or the car is slowing down faster than the design limites the system will cycle and not turn the light on. If say the back brakes are worn out the fronts may cycle the system as the front is the only thing stopping the car.

It may be a calibration issue. The sensor doesn't know what is considered slow or stop., Yes,your right, a computer thing.

on certain model when the ABS light come on the brake light come on as well. to see which sensor as set the ABS light you should have the code read with a scanner, you will be sure which sensor is defective

Sounds as if you have a false activation of the ABS system.
If the light does not come on until you are driving then the ABS module is probably seeing a difference in wheel speed from side to side. It could be caused by different size tires,are all your tires the same size and brand? It could be caused by one tire having low tire pressure. It could also be one of the sensor rings esp. on the front has maybe cracked and slipped out of place causing the air gap between the sensor and the ring to be larger than it is suppose to be.The gap between sensor and ring is usually 0.045 of an inch sometimes the ring which is pressed onto the outer CV joint will crack and the ring will slid up the joint slightly away from the sensor.This will decrease the amplitude of the sensor signal and ABS interputs this as a wheel trying to slip or lock up and activates the ABS.When ABS activates it will make a loud pulsing type sound and it will almost feel like it is not going to stop.