EDIT: beaten...
How do diprotic substances work in relation to pH?
For instance, if I have excess H2SO4, I understand it won't fully ionise to SO4^2- + 2H+
that is, all of the first H+ will be removed, but not all of the second - is that right?
How do we calculate the pH then?
Also, do bases have the same effect? For instance if I have excess Ca(OH)2, will it fully ionise to Ca2+ + 20H-
or will the second hydroxide ion not be released from all of the calcium hydroxide?
Re: sulfuric acid, since it is such a strong acid, you can assume the first ionisation is complete. You can then use this information to solve for the equilibrium of the second ionisation (if Ka is provided). Note that this is different to your normal acid/base equilibrium:

.....(1)

.....(2)

Let the initial concentration of 

. Reaction (1) is complete, so gives us 
,\tex{init}}\approx m)
 and 
,\text{init}}\approx m)
. The equilibrium expression therefore becomes
x}{m-x})
Which is a quadratic equation.
As you can see, this is a lot harder than your usual acid/base equilibrium questions. It is 
extremely unlikely that VCAA would ask something like this.
For weak, polyprotic acids (e.g carbonic acid, phosphoric acid), the situation is even more complex. Solving these systems require non-linear systems of two or three variables, which are usually computed numerically rather than exactly (i.e. we can't easily write down a formula for the answer).
As for Ca(OH)2, it is unlike a diprotic base that can exist in several deprotonated states (i.e. 1-, 2-, 3-, etc). Ca(OH)2 is a salt, so for the sake of ionisation in pure water, the salt crystal is either dissolved (all OH- is free) or it remains as an undissolved crystal (OH- not free at all).
If, however, we were to add acid, the acid would react with the dissolved hydroxide, and also eat away at any undissolved crystal. This is why acid rain can erode limestone.