Hi Kalpenj,
Congratulations on your visa grant.
I know this is a bit late for a reply, but I really wanted to reply to your questions.
1. State Nominated Visa is the reason you are allowed to work and live in Australia so I think you kinda owe it to South Australia to work and live in their state. I am aware that the job prospects are not so great (I too am struggling to get a full-time job for the past 6 months). But if you are sponsored by SA, I think you should come here and try to make it work here and then if (hope not) you can't make it, then you should think of changing states. Like NicF said, it is a moral obligation and not a legal one.
2. Once you have been granted your Visa, the case officer's job is done, thereafter any questions regarding your visa should be made to the department of immigration. And as for the completion of 2 years in the nominated state, you will be required to complete a survey once every 3, 6, 12, 18 and 24 months during the period of 2 years about living and working Adelaide. Any change of address or any of the contact details should be informed to the government. Once you have completed the 2 years, it is best to inform the state that you will be moving to another state. And your visa grant allows you to travel within Australia for 5 years without a problem so you do not need to apply for another visa.
3. However, you can apply for your citizenship after 4 years or get an RRV (resident return visa).
Also, if you do complete the 2 years in the nominated state, complete the surveys and keep the state informed about your details, it will reflect in the future when and if you do decide to apply for citizenship as your character display.
And, also I wanted to tell you something, on a different note. If you are planning to go to another state after being sponsored by one state, then you should've applied for the state you intend to live in. It is not morally correct towards SA and they might make it harder for other applicants to be nominated in the future.