Wrt tyre pressures;
Last time on the track we were doing 20 min on / 20 min off the track.
I've checked the tyres after a session (starting from 35psi ~2.4bar) and they were over 40psi. I've let out 4psi, and the car behaved very nicely. The 20 min wait wasn't enough to completely cool the tyres down, so it worked out well. But I did not get any faster

(although the traffic was always in the way, too)
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Toyota 86 GTS A/T, ACE 250/B header + OP, Apexi air filter, Whiteline camber bolts