You are not required to have health insurance for that particular visa, but of course insurance is always highly recommended, but it is not compulsory. Whoever told you that is wrong.
the Australian aged pension you are receiving cannot be transferred or willed to another person upon your death, each recipient of the aged pension must apply for it in person and pass the qualification rules to receive it. The widow pension is an old benefit and does not exsist anymore. So basically as your wife is neither an Australian citizen or permanent resident she will unfortunately receive no benefits upon your death, only what assets you leave to her in your will.
an Australian pension is not transferable to another person, every person who receives a pension in Australia must apply in person. You also cannot will you pension to another person, not even you wife.
any Australian pension is not transferable to another person. Each person must apply for a pension in Australia in person and follow the qualifications to apply for that pension. You can’t just transfer it to your wife, this is for Australian citizens, I have no idea how other countries do it, but the OP is asking about Australian pensions.
that is correct, the widows pension is a old benefit, and you cannot will your pension to another person, that person must apply for a pension on their own right, and follow the qualifications for the applicable pension.