More grip needs more compensation for understeer in RWD vehicles. Less grip + fast setup for better tires = oversteer. Same goes in reverse, a fast setup for lesser tires will understeer.
Normally. Sometimes a setup will become more oversteery with more grip due to the front biting in too hard and snapping the rear loose.
This is true, the extra grip racing tyres give can make the front turn more sharply, subesequently, the rear can be affected if it hasn''t been setup right or balanced out.
Alternatively the reverse can be true on lower powered cars, the extra grip and stability at the rear can sometimes 'numb' the front end.
I ws running a NSX at 460bhp on racing hards for a series I'm in, I went to a different friend's room and they were using a different PP system with racing soft tyres. I had to reduce the power and had more grip from the stickier tyres, I could feel the front end just wasn't as responsive as before and the car felt 'dead'. After adjusting some of the settings at the rear - trying to find the sweet spot between loosening the rear so the car will turn but leaving enough stability so it wouldn't loose grip and slide or spin, the car was doing far better lap times and was turning in, and through, corners so much better.
In my opinion you need to tune and setup each car individually, regardless of what tyres you're using - a 300bhp car compared to a 700bhp (both on racing soft) would probably have big diferences in certain area's of the setup.
4WD cars can be affected quite heavily too, some 4WD cars are very stable at the rear through corners or when lifting off the throttle, putting racing softs on the rear can add so much more stability the car can turn like a boat. But again, the amount of power (and weight) the car has is a factor also.
It's hard to come up with general rules that apply to all cars in all situations for all tracks, there is a absolutely huge amount of variables involved - even more if someone's driving style is to be considered as this is another important factor.
Just take each car individually - work out what areas of the suspension and LSD does what, what works in terms of correcting over or understeer and keep testing.
Don't be afraid to do something different too, for instance rear stability and grip, there are different area's of a car's setup that can have an impact on this, don't just try one thing, test using different methods and see what impact they each have on lap / race times and tyre wear.
As for specific areas of the setup:
LSD (all three)
Ride height
Roll bars
Toe
To be honest, I could say everything, in my opinion each area of the setup needs to work with everything else for the best results for that person's driving style in whatever car tuned to whatever level on whatever track. But those above 4 mentioned can make a huge difference - though the settings of everything else not mentioned would be important i.e.
Hard srpings and dampers would require slightly lower roll bar settings, soft srpings and dampers would require higher roll bar settings etc etc.
It's all linked together in my opinion.