Any question answered...

I think rolling resistance is determined by the amount of energy lost in deforming the tyre, would answer most of these questions. Smaller contact patch = less deforming, soft tyre= supple tyre conforms easier, thinner tyre = less deforming.

I'll wait for tester to explain why I'm wrong.

why are softer compound tyres faster than hard

but are they? I'd think softer compound would mean better grip but not necessarily more possible speed

some bro science below, but...

Presumably grip is needed for acceleration.
At one end you'd have an almost solid tyre that hardly deforms as it bounces over the imperfections on the road surface. For something like an indoor velodrome track then this works pretty well as you lose very little energy bumping over things. But you'd waste plenty by bouncing around on a gravel path, not to mention sliding out as the tyre fails to hold on.

Then as you get a wider tyre and a lower pressure then you can deform around/deal with the imperfections of the road surface. And the ideal tyre depends on the road surface.

And the added reassurance of a tyre feeling more sure footed will lead to a rider pushing a bit more than they might on a rock solid tyre on sketchy ground. So there'll be a crossover where a technically faster tyre probably ends up slower in the hands of 99% of riders/drivers who value the confidence inspired by the marginally slower tyre.

Also why is a thinner tyre faster than a thicker one

What do you mean by thinner and thicker?
Since we're on a bicycle forum, I'm assuming you're only talking about tyres of essentially circular cross section with very compliant carcasses, all most bets are off once you switch to square rigid tyres.
As other respondents have already intimated, there's a lot of difference between pure rolling resistance (mostly hysteresis, measured on a steel roller) and resistance to forward motion on a practical surface, where suspension losses become a significant or, in some situations, dominant factor.