Jack the front of the car up, grab the right front tire at top and bottom and pull and push for any play. Repeat when holding the tire at the sides. If you feel a slight amount of play in both directions you probably need a new wheel bearing. If you only feel play when grabbing the tire at the sides it could be a tie rod end. The other symptom of a bad bearing on the right is the noise will be worse when turning left, since that puts the most stress on the right bearing.
The pulsating in the braking is likely warped brake rotors. Replace rotors and pads.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)