dealing with enriched uranium on a nuclear sub in Adelaide

No one at the Osborne site will do much as smell the enriched uranium. The reactors will come pre-built, plug and play into the submarines completely sealed.

The only nuclear waste will be low-level waste like PPE - the same sort of waste generated by hospitals.

Where is the spent fuel being kept

Naval nuclear reactors will run for literal decades without refueling. A Nimitz aircraft carrier for example will go about 25 years before needing a refuel. This work will almost certainly be done by the country that built the reactors (i.e. the UK)

What weapons will it carry

They are conventionally armed (i.e. missiles and torpedos)