
You can generally work for up to 20 hours a week during term time, and full time during holidays. Permission to work is not automatically given with your first student visa, you must get this added to your visa by DIMA once you prove to them you have begun study in Australia. Your dependents may have the right to work as well, depending on the course you are studying and what country you are from DIMA Factsheet 50 Overseas Students
Bear in mind that most students, even with limited work rights, only get casual and poorly paid work in Australia. The effect of working on your studies must also be considered. You should not rely on working to support yourself.
As of the 1 July 2000, the answer is no. It used to be possible, and applications submitted before 1 July 2000 will still be processed and existing visas will be allowed to continue through to expiry. Australia is in negotiations with a range of additional countries to establish reciprocal working holiday arrangements.
Your UK passport must describe you as a British Citizen to participate in the scheme for UK nationals. Other British passport holders, including British Dependent Territories citizens and British Overseas citizens are not eligibl, although most people from current British territories acquired full British citizenship 21 May 2002 (they should acquire British citizen passports to be eligible). British Nationals (Overseas) are not eligible to be treated as UK nationals, but can apply for the scheme recently set up with Hong Kong.
The only restriction is that you must apply for the visa before your 31st birthday. Subject to this, it's not important when the visa is granted, or when you actually travel to Australia (provided you abide by the entry date given on the visa).
No. Although you can choose which nationality to apply on the basis of (for some countries you must apply in the country of citizenship, for others this requirement does not apply) you cannot get a second WHV once you have used the first one to enter Australia. Obtaining a second WHV constitutes visa fraud and will set you up for mega-problems either immediately or later when you want to settle in Australia.
As long as you are eligible for an Australian WHV, the fact you have had a NZ WHV is irrelevant.
No. If both spouses are to hold WHVs, then both must meet the requirements in their own right. Your spouse will be able to accompany you to Australia, but will have to use another visa - eg tourist status, and abide by the conditions of that visa.