Hi Stein, I suspect problem is question is to broad and very directly relates to your driving style and specific setup.
Without knowing spring rates etc it is very hard.
My first thought for the road course is have you bled your brakes and put in hi temp fluid and pads and/or bigger brake setup?
My friend with an LS1 (?) has terrible brake issues on our road courses. Brakes catching fire, fading to nothing etc and this is WITH a 6 pot willwood and 11.5 - 12" rotor and the correct pads (well race pads, correct is still questionable...). A V8 Mx5 is a VERY fast car on the track.....think close to Porsche GT3 speeds (maybe one with an average driver...
Tyre pressures we end up running are anywhere from 23 - 30 psi on dunlop 03g/toyo r888 type tyres but varies tremendousley on track type, ambient and track temp, type of tyre (no experience with RS3's) and how long each session is......I can get my tyres close from looking at them after a session but I spent years road racing motorcycles....where tyres are your life!
You want a slight amount of rubber rolling off the outside of the tyre, and the surface looks a bit like 200 grit sandpaper but ****, hard to explain....(gonna get nailed for that descriptpion I suspect)
Try and talk to someone who is religousley measuring tyre pressure/temps at the beginning of the day and after each session. They will most likely point you in the right direction...people who just show up and drive...not so much.
As far as suspension goes I would imagine full stiff at both ends and reduce at either end from thereon for balance (pointy, tail'y....). I would think Teins with standard rates are TOTALLY unsuitable for a v8 Mx5 on the track (still to soft) but you will still have fun (while you have brakes at least....)
You might also want to lower the car (but don't go crazy), this might help reduce roll and pitch making braking and cornering a bit more pleasant.....of course this needs a new wheel alignment (See 949racing.com for suggestions on wheel alignment for track cars).
For the strip probably reduce rear to full soft for weight transfer at launch..? Could even raise the car a little to promote further weight transfer...?
Very vague but hopefully helps or initiates someone with more experience than me to chip in and correct my errors
Most of all have fun, take it easy on the car and it should be an awesome day.