Occurrence of vibration on the steering while braking is an indication of misalignment of front pad and disc. Front brakes are connected to the steering wheel thru the front end, that’s why when there is a problem on front brakes it will be detected thru the behavior of the steering wheel.
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For power steering car, this kind of problem often trace to a faulty power steering pump, power steering cars are equip with power steering pump that pumps a power steering fluid to create hydraulic force, this hydraulic force is applied to the steering gear box causing the steering of your car a lot easier, when your car steering pump occasionally fails and will stop pumping for a moment, there will be no hydraulic pressure applied thereby causing your car steering momentarily becomes stiff.
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Steering wheel looseness problem often resulted from a loose steering column bracket or universal joint or coupling.
As you may not know the steering wheel is connected to the steering shaft that is connected by a coupling or universal joint to the steering gear, this steering shaft is surrounded by steering column that is secured by a steering bracket.
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