Winz give you money to pay for housing, you can't make yourself homeless and then use that housing money to pay for something else. The reason they cut the benefit is because the funds are not being used as intended. Generally if you become homeless while on a benefit you're meant to notify them immediately, and they can arrange accommodation (often put people in motels). I'm sure most people don't bother doing this as winz would usually be aware that you're homeless.

Unfortunately winz is automatically notified of these types of changes through the police.

Winz are jerks about cars. If you had a job offer that required a car they would then assist you. But until then you're expected to use public transport or walk. If public transport isn't avaliable you can apply to them for assistance to attend an interview (with proof).

I hope you get a job soon. I recommend you try to get an emergency appointment with winz (they can reinstate) and say your accommodation fell through rather than you chose to leave.