You only need to do your 90 day report when you spend 90 consecutive days in Thailand, if you leave before that the 90 days start again from the day of entry which is day 1.
That entirely depends on your local immigration office some will definitely want to see your up to date TM30 some will not, best to go and ask them, or just get your landlord to do it for you anyway.
No, as a Australian passport holder you get a 60 day visa exempt stamp in your passport free of charge when you arrive here, you can also get a 30 day extension at your local immigration office for 1,900 baht if you require to stay longer.