Kandice, you are well within your rights to serve your landlord with a 10 day notice to fix the issues in the house.
It basically gives her 10 days to sort the most important items out. It doesn't matter if you have an agreement or not. If she doesn't do it within that time period then you go to mediation. The mediator will then rule on what she needs to fix. This may take awhile as she may have to provide quotes and/or you will have to provide quotes. Most companies will quote to have bulk items fixed.
Also in Auckland to replace a low pressure cylinder not including the valves can cost between $1300 - $1500+GST. Not sure what it would be down there as I don't know what the hourly rates are for plumbers down your way. The hot water cylinder if over 25 years old should be replace, is there any rust around it? Cylinders can be dodgy because of the calcium, they can cause the cylinders to break down and also for the water to be not so good.
Another hint for you; when you fill your jug dont' use the hot tap, use the cold tap. It may take longer for the jug to boil, but the water you will be getting from the cylinder will be from the bottom.
Our company would charge approx $300 to replace the light switches, so that's about what Cuppatea estimated also.
Personally I'd be going for 10 day notice.