[Xracer]

Mmm a list to contend with there but I can try and add some light that I hope concurs with the thoughts of others.

First and probably a good starting point in Shore hardness, this is the measured hardness of the raw sheet material from which the tyre rings are cut, the lower the Shore number the softer the rubber compound.
The tyre hardness will vary from the outside to inside as the rubber is stretched onto the wheel, the bigger the starting diameter the softer the tyre will be but attempting to measure a actual tyre hardness is not a true Shore measurement but can only really indicate a difference from one tyre to another, not the actual true Shore value but an indicator only.
As the tyre wears or is trued down the actual hardness will increase slightly because of the pre-stretch onto the rim.

I believe it is commonly considered that the smaller the tyres the better the cars handle mainly due to the lowering of the roll centre of the car, there may be more debate on the actual physics of this to follow.

I am led to believe that starting at 44-45 mm for the rear and 1-1.5 mm smaller on the front will deliver a good handling car and give some degree of tyre life, assuming you don't 'chunk' them on the barriers in the meantime!
The softer tyres can chunk very easily unless some reinforcement of the tyre edge is carried out, some use superglue, some use Shoo Goo or an equivalent.

I have also found that as supplied the tyres are not always very true, I have had some up to 1 mm eccentric, so a truer is needed initially as this plays havoc with the cars handling.

When it comes to tyre wear then this depends of a lot of factors, circuit layout i.e. sharp corners or sweeping curves, driving style, aggressive or smooth, repeated application of additive rather than changing tyres for each heat as some do.
The actual rubber compound being used will deliver differing wear rates irrespective of the original shore hardness too.

I have measured tyres to try and establish wear rates and I have seen somewhere between 0.2-0.5 mm per heat, depending on the tyre hardness being used, the carpet type, condition and grip level, surprisingly the higher rates were measure when racing without additive on 32 Shore tyres though!

As for tyre truers, there are a number on the market, sometimes hard to get hold of but Hudy, 3Racing, Integy, Fastrax to name just four and of course you will need suitable mandrels depending on the wheel type you are using.

I hope this goes part way to answering your emerging questions.