The springs should be butted up againstbthe end stops on the lower cups.
The handling and noise are not connected IMO.
It could be something as simple as tyre pressures being wrong, or even down to the make of tyre, grabbing and pulling over uneven surfaces is quite normal for some cars to do dependant on which tyres they have, some cars are more prone to this, than others, due to lots of different factors, how hard the suspension is is one of them.
It is immensley hard to determine where on the car the noise is coming from, but sounds more like, either areally bad wheel bearing allowing the disc to tilt and rub, or the transmission, it is too fast a grinding noise for driveshafts, but it would seem to be due to being worse on full lock.
My money would be on having a CLOSE look at the wheel bearing on the noisy side first.
tabetha