It stops it from stepping out so often, wider track = more grip
Are you sure Ad Lav because really you still got the same contact area you've only pushed the lever arm out more.
You'd get more grip if you went for a 225 tyre and alloy to match.
Yup, a wider track will give the back more grip, plus having good tyres helps even more, I know what you mean though
It stops bodyroll and helps keep the car level through corners/balanced so it goes better.
It doesnt actually provide more grip, as said the contact between road and tyre stays basically the same. But you are right in that it will provide better stablility and control.
Technically it will reduce body roll in two ways. one simply due to the track being wider compared to the body and weight distribution, but the way the rear behaves will alter, (with wider track it will be slower).
Imagine somone on a tightrope, when your balance needs adjusting you have to move very fast, but if you have a wider track, (imagine the long poles they sometimes use) the correction is slower and more deliberate.
As a result the rear is less twitchy and more difficult to upset.
As standard the rear is narrower that the front by a considerable margin, this means the rear acts faster and is more twitchy than the front, which can catch people out, particularly if a bump catches the car at the wrong time.
Another missconseption is that harder suspension provides more grip. It doesnt. Tyres provide grip, the way its used is controlled by the suspension.
The main area that harder suspension provides gain is how quickly it provides the grip, ie if you turn in there is a delay where the suspension compressed and the tyre also compressed before the grip is provided. Softer suspension therefore has longer delay and this difference is exagerated when changing direction.
However, too hard and the suspension may apply the grip too quickly (or if you just jank the wheel round), or may not be able to accomodate anything other than smooth surfaces. (softer suspension is often faster in wet conditions for example)
Anyone old enough to remember renault 5 turbos will know that especially when lowered they would skip over bumps, as the suspension could not accomodate bumps. Many people found this to their ultimate cost.