DOT stands for Dept of Transport which refers to the USA Federal DOT and is not an Australian requirement or reg. Ditto 'Not For Highway Use' on a tyre. Neither are of any legal or regulatory significance in Oz.
In NSW, and I think all of Oz, the only rego requirement is tread (1.5mm minimum) and of sound construction (no visible damage (normally meaning you can't see the 'carcass' or construction cords of the tyre)).
Nope. Wrong on most counts, even.
Tyres used on the road need to be approved for on road use - and marked as such.
Australia has its own standards, but will also accept certain overseas standards - including the DOT standard. The grey import cars coming out of Japan almost always need their tyres changed before they can be rego'd here - either the Japanese standard isn't recognised, or there simply isn't one in Japan.
Further, tyres marked "off highway use only" or "NHS" will be defected by a suitably motivated copper, no matter how much tread depth they have. And rego will knock them back, in both NSW and ACT.