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.
Start with around 50 front/35 rear for a GT, 50 front/35 rear for a Zen. Go down on the front for more steering, and up on the rear for more rotation.
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.
Not strictly true. Hardness will vary depending on where the tyre is cut from the sheet. Stretching it over the rim makes little difference. As stated, there is a variation on tyres with the same hardness number on the label, but not so as you need to worry about it.
As the tyre wears or is trued down the actual hardness will increase slightly because of the pre-stretch onto the rim.
More effect is seen from the fact that as the tyre gets smaller it moves round less on the track. Smaller tyres make the car more precise in handling. Anything from 46 rear/44 front downwards is OK, bigger than that will make the car feel imprecise.
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.
See note above. Tyre diameter has no impact on roll centre as the main weight of the chassis is always in the same place relative to the roll centre due to ride-height adjustment. Again, less tyre means more precise handling, but the roll centre is not the cause of that.
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.
GT12 tyres are pretty robust; I find Contacts the best in this respect. It pays to run a bead of superglue across the tyre/wheel joint (Zen have an excellent range - e-mail them for recommendations) on the rear. For the fronts, run superglue right up the sidewall until it meets the tread. This prevents the car rolling and makes it handle much better.
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.
Too right!!
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!
I get a bit less than that per race, but it really does depend on the carpet and the additive. SXT 3.0 is good just about everywhere. When the grip comes up them Spider Grip Green is better.
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.
If you can't run to a tyre truer, then see if someone at your club will bring theirs along or do some tyres for you. Once you have them at the starting point, there's little need for the truer until you need to restore the stagger (difference between front and rear diameters) as the rears usually wear faster than the fronts. Less stagger gives more rotation, but only up to a point. Fronts should NEVER be bigger than rears. Don't sweat on not having a truer - make a friend of someone and use theirs. Coffee and beer for your time on a truer usually smooths that path! If you are anywhere near the Shootout series at Chesterfield club, come along and someone will sort you out for free. 
I hope this goes part way to answering your emerging questions.