I can't comment on the Centrelink issues and how they are linked to visas and partner status. But in general, if you are in Australia on a valid visa (eg Working Holiday Visa) and without further stay condition, you can apply onshore for the 820/801 Partner Visa (assuming that at that time you qualify for the defacto relationship requirements). Once your existing visa expires, you automatically get a bridging visa whilst you wait on the outcome of your partner visa application. This briding visa comes with full work rights. However, be careful that you don't misrepresent your intentions when applying for the original visa to Australia.
Another alternative you can consider is to apply offshore for the Prospective Marriage Visa, move to Australia and then apply to the 820/801 once there. The Prospective Marriage Visa is intended exactly for those people who do not yet qualify for a defacto relationship status. You cannot apply for this visa onshore though.
It sounds like you need some more clarity on visa options so it is a good idea to consult with a Registered Migration Agent (RMA). This can but does not need to be an immigration lawyer. If you get an Australia based RMA (several recommended ones post on this site) they can give professional advice on options.
One final thing to note - being in a defacto relationship does not require you to live together, but expect any period apart to be scrutinised. Consulting with an RMA will also be helpful for you to understand exactly what the evidence requirements are.
Last edited by taco; 08-21-2018 at 04:27 PM.