Australian moving to Germany tax and tax treaty questions

I will be moving to Germany to take a position. I have some tax related questions. Here is my situation: I am an AU citizen. My wife is a dual AU/DE citizen. We have a mortgage on our family home in AU. My (lots of) questions are:

   1. Initially, I will be starting work in Germany, whilst my wife will remain working in AU. Earning about the same. What is the most beneficial combination for us; file separate tax return in the respective countries where we work? Would I then be considered Category I in Germany as my wife lives apart? Should we file jointly in one of the countries? which one?
   2. Later, my wife will join me in DE. She will likely be unemployed for a while and then earn less than me initially. Should we then file tax return in DE, where I am class IV and she is III?
   3. There is a new tax treaty between AU and DE ( here). I don't understand it. Can anyone explain how this affect my situation?
   4. Article 19 of this treaty says that professorships are exempt somehow. Can anyone explain what this means?
   5. I called the ATO to enquire. They told me that if I remain an AU resident, I will have to pay any gap in the level of taxation between the countries in AU. Is that right? Would it be more beneficial to seek residence in DE then?
   6. Whilst living in DE, our AU family home will be rented out. The ATO told me that I will have to pay tax on the rental income, but won't be able to claim against the rental I will be paying in DE. Sounds a bit unfair, but anyway, should I be able to claim the mortgage payments against the rental income? Would it be better to declare the rental income and mortgage cost in my DE tax return?
   7. The ATO also said something about additional tax, if I later sell the house and haven't returned to AU within 6yrs. Can anyone explain better than the ATO?

This is all so complicated and overwhelming for me. Any advice would be much appreciated.