Second, you said:"Using the tax calculator someone posted the...

Second, you said:

"Using the tax calculator someone posted the link for here,it seems that if i claim resident in Oz for 1 month of the year,i get the tax free threshold and pay the medicare levy."

There are certain conditions that you need to satisfy before you become a "resident" for income tax purposes. I don't think you can become a resident for tax purpose by deciding for yourself that you are going to "claim resident in Oz for 1 month of the year ..", it is not that simple :-)

Also, there is residency for income tax purposes and there is residency for immigration purposes, both of which have different qualifying requirements. Do not get the two confused; they are not the same.

It will be in your best interest to seek professional advice.

All the best.