JA are doing deals at the moment when you buy a hand held GPS unit they throw in free garmin topo maps check it out here
Free Garmin Topo Australia and New Zealand
I'm pretty sure tyres have a statutory warranty of 5 years from purchase date (I know this to be the case with my local tyre place ) , would be having a chat to the retailer, if no luck might be worthwhile contacting the Tyre and Rim association.
Looking at Tracks4Aus there is a track about 2-3 kms west of Katoomba along the highway (looks like it is called Nellies Glen ) which heads down to Euroka which then crosses the Cox's River and heads to Black Range which then takes you to the Jenolan Caves Rd.
Doable ? no idea but it is on the map.
haven't used androzic but think it's a thinly disguised copy of oziexplorer , that being the case there should be a folder in there called 'maps' just drop them in there i would guess.
You can get a tool known as a nylon strap oil filter removal tool, it works with the use of your half inch socket, this is the only removal tool that has never let me down. about $20 from repco supercheap etc
just needed that one more post before i could enter links so here it is
http://www.quarantinedomestic.gov.au/images/stories/pestsdiseases/ffez-map2.jpg
Isn't the Bendelby Ranges on private property, help should be at hand if you need it. Also should be plenty of others up that way so I don't think you'll have any issues.
looking for similar myself, best choices probably garmin and magellan outdoor handhelds, have a look though the gpsoz site, they have them all, some come with extra 'adventure packs'