I am living in S.A. but soon to be paid from Australia. Just trying to work out my tax implications.

If you are performing work in SA and are a SA tax resident then you would need to pay tax in SA regardless of where the money is paid. You also need to have permission to have a foreign bank account so I suggest having the money paid into your SA account.

So I am an Australian citizen, but a South African Permanent resident. I was not aware that I would need permission to still have my Australian bank account - who do I get that permission from. Then if I am getting paid from Australia and I have to pay tax here, don't I also have to pay tax in Australia, which would mean getting taxed twice?

Apologies, I didn't know you were an Australian resident. It would depend where you are tax resident, but usually you pay tax on the income earned from services rendered in the country were you worked and can use this as a tax credit in other places if you are taxed twice. As an Australian resident you will still be able to have any bank account wherever you are.