Hi Jil,The weather here in aus can get very hot in the summer ,up to 40c.
I have attached a link for the australian weather website showing the average temps in different parts of the country.

Australian Weather Calendar

Then if you click on the individual states shown on the top right of the page(where it shows NSW VIC QLD WA etc ) it will show the current forecasts for those states.
The north of australia in summer is the wet season.Hot,humid,wet and prone to cyclones so if starting in perth heading across the bottom of australia to south australia then heading north through victoria and nsw would be the best bet.
fuel stops when crossing the eyre hwy are around 200 klms apart so make sure the bike you buy can exceed that distance as strong headwinds will use more fuel,or carry extra fuel.
The most popular website for buying motorcycles here is gumtree.

Perth Region, WA | Motorcycles & Scooters | Gumtree Australia Free Local Classifieds

paying cash is usually the preferred method.

The cost of registration for a motorcycle in western australia is $355.10 for 12 months or $104.30 for 3 months.

As long as the bike is registered it is valid after the sale in the state the bike is registered in(if the bike is registered in WA and is bought in WA then the registration on it is valid).you will need to fill in a form with the seller at the time of purchase that says you are the new owner.
We have recently had personal insurance included in the registration for accidents but it may be a good idea to have your own travel insurance as well that covers you for riding motorcycles.

regarding your other questions i am sure someone more knowledgeable will be able to help.