Can the council kick us out of our shed/house?
Potentially, yes. Although this is very unlikely.
Does the amount of time we've lived here make any difference?
No.
The law that governs building and construction in NSW is the Environmental Planning and Assessment Act 1979. It's a very broad law and covers everything from a flagpole or barbeque to airports and railways and has a hierarchy of controls from State Environmental Plans (SEP) down to Local Environmental Plans (LEP) and finally the Building Code of Australia (BCA) and Plumbing Code of Australia (PCA). Electricity and gas installations are covered by different laws.
However, for housing, there is a SEP that allows them to be constructed without Development Consent providing they comply with all relevant LEPs and the BCA & PCA. These so-called Complying Developments (CD) must be notified to the council but do not need the Council's approval. If you want to break the rules, you can't use this process and must go for a full Development Approval (DA). For completeness, there are also Exepnt Developments and State Significant Developments but neither are relevant here.
Once you have your DA or CD, you need to engage a Principal Certifying Authority (PCA) - a private certifier who ensures that the work is in compliance with the DA/CD and the BCA. They will issue a Construction Certificate (CC) which details the work that needs to be done. When its all finished to their satisfaction, they will issue an Occupation Certificate (OC) and the building can now be used.
You state that you have a DA (or maybe a CD) for a house and shed but only the shed was built and then fitted out as a house. Prima facie, this isn't compliant because it isn't what was approved. I am willing to bet that there is no OC and possibly no CC. This happens a lot.
When you brought the property, your conveyancer should have checked that all building work was compliant. Maybe they did and told you about it but you didn't understand and went ahead anyway; maybe they didn't and just stuffed up.
Now, if the building complies with the LEP and the BCA, all that may be necessary is to lodge a CD, hire a PCA to inspect the property and issue an OC and all the paperwork will be in order and everyone's happy.
If there are non-compliances, the council can, and probably will issue you a notice to fix them within a specified time frame. Providing you do that, you can then get the retroactive approvals and all will be good.
However, if it's something that can't be readily fixed - like the building is too near the boundary, for example, that's when things get interesting.
